Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
49201	Solve the Function Operation	If f(x)=2x and g(x)=2x^2-1 find f(g(x))	If $f (x) = 2 x$ and $g (x) = 2 x^{2} - 1$ find $f (g (x))$
49202	Solve the Function Operation	Given that f(x)=x^2-11x+18 and g(x)=x-9 ; find f(x)+g(x) and express the result in standard form.	Given that $f (x) = x^{2} - 11 x + 18$ and $g (x) = x - 9$ ; find $f (x) + g (x)$ and express the result in standard form.
49203	Find the Domain	(5x)/(3x(x+12))	$\frac{5 x}{3 x (x + 12)}$
49204	Find the Domain	f(x)=4/(1-2 natural log of x)	$f (x) = \frac{4}{1 - 2 \ln (x)}$
49205	Find the Asymptotes	(x+3)/((x-1)(x+3))	$\frac{x + 3}{(x - 1) (x + 3)}$
49206	Solve the Function Operation	f(x)=-8x-9 ; find f(-3)	$f (x) = - 8 x - 9$ ; find $f (- 3)$
49207	Solve the Function Operation	If f(x)=x+7 and g(x)=3x-5 ; what is (f+g)(x) ?	If $f (x) = x + 7$ and $g (x) = 3 x - 5$ ; what is $(f + g) (x)$ ?
49208	Find the Domain	cube root of 9-x^2	$\sqrt[3]{9 - x^{2}}$
49209	Find the GCF	10x and 25	$10 x$ and $25$
49210	Solve the Function Operation	f(x)=(x-2)^2-1 if x!=0; 4 if x=0 Find f(0)	$f (x) = {\begin{cases} {(x - 2)}^{2} - 1 & x \neq 0 \\ 4 & x = 0 \end{cases}$ Find $f (0)$
49211	Solve the Function Operation	g(x)=2x-5 h(x)=4x+5 Find g(3)-h(3)	$g (x) = 2 x - 5$ $h (x) = 4 x + 5$ Find $g (3) - h (3)$
49212	Solve the Function Operation	f(x)=-x^3 , (f(a+h)-f(a))/h	$f (x) = - x^{3}$ , $\frac{f (a + h) - f (a)}{h}$
49213	Find the Asymptotes	f(x)=(x-6)/(x^2-6x)	$f (x) = \frac{x - 6}{x^{2} - 6 x}$
49214	Solve the Function Operation	f(x)=2x^2-5x+10 g(x)=-2x-3 Find: f(g(x))	$f (x) = 2 x^{2} - 5 x + 10$ $g (x) = - 2 x - 3$ Find: $f (g (x))$
49215	Find the Asymptotes	f(x)=(x^3-2x^2-8x)/(3x^2-27)	$f (x) = \frac{x^{3} - 2 x^{2} - 8 x}{3 x^{2} - 27}$
49216	Find the Domain	2tan(x)^2=2cot(x)+1	$2 \tan^{2} (x) = 2 \cot (x) + 1$
49217	Solve the Function Operation	f(x)=-3x-14 g(x)=3x^2-x+15 Find: (fog)(x)	$f (x) = - 3 x - 14$ $g (x) = 3 x^{2} - x + 15$ Find: $((f \circ g)) (x)$
49218	Find the Domain	(a^2)/(ax-x^2)+x/(x-a)	$\frac{a^{2}}{a x - x^{2}} + \frac{x}{x - a}$
49219	Solve the Function Operation	g(a)=3a+2 f(a)=2a-4 Find (g/f)(3)	$g (a) = 3 a + 2$ $f (a) = 2 a - 4$ Find $(\frac{g}{f}) (3)$
49220	Solve the Function Operation	f(x)=2x^2-5x-8 g(x)=-5x+4 Find: (gof)(x)	$f (x) = 2 x^{2} - 5 x - 8$ $g (x) = - 5 x + 4$ Find: $((g \circ f)) (x)$
49221	Find the Asymptotes	f(x)=(9x^2)/((x-1)(x+2))	$f (x) = \frac{9 x^{2}}{(x - 1) (x + 2)}$
49222	Solve the Function Operation	cos(theta)=-24/25 , theta in quadrant II	$\cos (θ) = - \frac{24}{25}$ , $θ$ in quadrant $I \cdot I$
49223	Find the Asymptotes	(25x^2-64)/(10x^2+16x)	$\frac{25 x^{2} - 64}{10 x^{2} + 16 x}$
49224	Determine if Odd, Even, or Neither	F(x)=-x^4+2x^2+8	$F (x) = - x^{4} + 2 x^{2} + 8$
49225	Solve the Function Operation	f(x)=-(x+2)^2+8 if x!=-5; 0 if x=-5 Find f(1)	$f (x) = {\begin{cases} - {(x + 2)}^{2} + 8 & x \neq - 5 \\ 0 & x = - 5 \end{cases}$ Find $f (1)$
49226	Find the Domain	(a-2)/(8a)+(2a+5)/(8a)-(3-a)/(8a)	$\frac{a - 2}{8 a} + \frac{2 a + 5}{8 a} - \frac{3 - a}{8 a}$
49227	Find the Domain	(a^3-b^3)/((a-b)^2)+(3ab)/(b-a)	$\frac{a^{3} - b^{3}}{{(a - b)}^{2}} + \frac{3 a b}{b - a}$
49228	Solve the Function Operation	f(x)=x^2+5x-11 g(x)=-2x+1 Find: f(g(x))	$f (x) = x^{2} + 5 x - 11$ $g (x) = - 2 x + 1$ Find: $f (g (x))$
49229	Find the Slope	(9,8) and (5,1)	$(9, 8)$ and $(5, 1)$
49230	Solve the Function Operation	f(x)=2x^2-2x+4 g(x)=x+6 Find: (fog)(x)	$f (x) = 2 x^{2} - 2 x + 4$ $g (x) = x + 6$ Find: $((f \circ g)) (x)$
49231	Solve the Function Operation	f(x)=x^2+7x-1 g(x)=-2x-9 Find: (fog)(x)	$f (x) = x^{2} + 7 x - 1$ $g (x) = - 2 x - 9$ Find: $((f \circ g)) (x)$
49232	Solve the Function Operation	f(x)=-2x+10 g(x)=3x^2+5x+14 Find: f(g(x))	$f (x) = - 2 x + 10$ $g (x) = 3 x^{2} + 5 x + 14$ Find: $f (g (x))$
49233	Solve the Function Operation	f(x)=2x^2+6x-7 g(x)=-2x-3 Find: (fog)(x)	$f (x) = 2 x^{2} + 6 x - 7$ $g (x) = - 2 x - 3$ Find: $((f \circ g)) (x)$
49234	Solve the Function Operation	f(x)=x^2-2 if x!=0; -6 if x=0 Find f(-1)	$f (x) = {\begin{cases} x^{2} - 2 & x \neq 0 \\ - 6 & x = 0 \end{cases}$ Find $f (- 1)$
49235	Solve the Function Operation	f(x)=2x^2-x+12 g(x)=-3x-4 Find: (gof)(x)	$f (x) = 2 x^{2} - x + 12$ $g (x) = - 3 x - 4$ Find: $((g \circ f)) (x)$
49236	Solve the Function Operation	f(x)=x^3+2 ; find f^-1(x)	$f (x) = x^{3} + 2$ ; find $f^{- 1} (x)$
49237	Solve the Function Operation	f(x)=(x+9)^3 ; find f^-1(x)	$f (x) = {(x + 9)}^{3}$ ; find $f^{- 1} (x)$
49238	Solve the Function Operation	Let f(x)=x^2-16 and g(x)=x+4 Find f/g and its domain.	Let $f (x) = x^{2} - 16$ and $g (x) = x + 4$ Find $\frac{f}{g}$ and its domain.
49239	Solve the Function Operation	f(x) = fifth root of x+2 ; find f^-1(x)	$f (x) = \sqrt[5]{x + 2}$ ; find $f^{- 1} (x)$
49240	Find the Asymptotes	(5x^2-45x+100)/(-4x^2+20x)	$\frac{5 x^{2} - 45 x + 100}{- 4 x^{2} + 20 x}$
49241	Solve the Function Operation	If f(x)=4x-3 ; what is f(x)^-1 ?	If $f (x) = 4 x - 3$ ; what is $f {(x)}^{- 1}$ ?
49242	Solve the Function Operation	f(x)=-2x-5 g(x)=x^2+6x+2 Find: (gof)(x)	$f (x) = - 2 x - 5$ $g (x) = x^{2} + 6 x + 2$ Find: $((g \circ f)) (x)$
49243	Find the Slope	(-1,-6) and (-5,10)	$(- 1, - 6)$ and $(- 5, 10)$
49244	Solve the Function Operation	f(x)=-4 if 2<=x<6; 4 if x=6; -(x-7)^2 if x>6 Find f(3)	$f (x) = {\begin{cases} - 4 & 2 \leq x < 6 \\ 4 & x = 6 \\ - {(x - 7)}^{2} & x > 6 \end{cases}$ Find $f (3)$
49245	Find the Domain	(2x+bx-2y-by)/(7x-7y)	$\frac{2 x + b x - 2 y - b y}{7 x - 7 y}$
49246	Solve the Function Operation	f(x)=10 fourth root of x ; find f^-1(x)	$f (x) = 10 \sqrt[4]{x}$ ; find $f^{- 1} (x)$
49247	Solve the Function Operation	Given that f(x)=x^2+17x+70 and g(x)=x+10 ; find (f+g)(x) and express the result in standard form.	Given that $f (x) = x^{2} + 17 x + 70$ and $g (x) = x + 10$ ; find $(f + g) (x)$ and express the result in standard form.
49248	Find the Domain	f(x)=(1+x^2)/(2-e^(3x+1))	$f (x) = \frac{1 + x^{2}}{2 - e^{3 x + 1}}$
49249	Solve the Function Operation	f(x)=-1/2x-1 if x<-2; x+2 if -2<=x<=3; -2x+7 if x>3 Find f(-2)	$f (x) = {\begin{cases} - \frac{1}{2} x - 1 & x < - 2 \\ x + 2 & - 2 \leq x \leq 3 \\ - 2 x + 7 & x > 3 \end{cases}$ Find $f (- 2)$
49250	Solve the Function Operation	f(x)=x^2-4x+6 g(x)=-3x+1 Find: (gof)(x)	$f (x) = x^{2} - 4 x + 6$ $g (x) = - 3 x + 1$ Find: $((g \circ f)) (x)$
49251	Solve the Function Operation	f(x)=(x^(1/2))/7 ; find f^-1(x)	$f (x) = \frac{x^{\frac{1}{2}}}{7}$ ; find $f^{- 1} (x)$
49252	Find the Domain	((a^2+ax+x^2)/(ax+2ay))÷((a^3-x^3)/(bx+2by))	$\frac{a^{2} + a x + x^{2}}{a x + 2 a y} \div \frac{a^{3} - x^{3}}{b x + 2 b y}$
49253	Solve the Function Operation	g(a)=2a-1 h(a)=3a-3 Find (g*h)(-4)	$g (a) = 2 a - 1$ $h (a) = 3 a - 3$ Find $(g \cdot h) (- 4)$
49254	Solve the Function Operation	f(x)=x^2-4x+32 ; at (3,0) , t^3	$f (x) = x^{2} - 4 x + 32$ ; at $(3, 0)$ , $t^{3}$
49255	Find the GCF	14 and 28	$14$ and $28$
49256	Find the Asymptotes	F(x)=3^(x-2)+1	$F (x) = 3^{x - 2} + 1$
49257	Solve the Function Operation	f(x)=-x+1 if x!=4; 6 if x=4 Find f(-5)	$f (x) = {\begin{cases} - x + 1 & x \neq 4 \\ 6 & x = 4 \end{cases}$ Find $f (- 5)$
49258	Solve the Function Operation	f(x)=3x^2+6x+5 g(x)=-x+3 Find: f(g(x))	$f (x) = 3 x^{2} + 6 x + 5$ $g (x) = - x + 3$ Find: $f (g (x))$
49259	Find the Asymptotes	f(x)=tan(pi/2x)	$f (x) = \tan (\frac{π}{2} x)$
49260	Solve the Function Operation	Given h(x)=5x+2 ; find h(-6)	Given $h (x) = 5 x + 2$ ; find $h (- 6)$
49261	Solve the Function Operation	g(x)=x-11 ; Find g(25)	$g (x) = x - 11$ ; Find $g (25)$
49262	Solve the Function Operation	f(x)=x-7 g(x)=3x^2-7x-10 Find: (fog)(x)	$f (x) = x - 7$ $g (x) = 3 x^{2} - 7 x - 10$ Find: $((f \circ g)) (x)$
49263	Find the Slope	(9,-4) and (1,-4)	$(9, - 4)$ and $(1, - 4)$
49264	Solve the Function Operation	f(x)=x^2-7x-9 g(x)=-5x-11 Find: (gof)(x)	$f (x) = x^{2} - 7 x - 9$ $g (x) = - 5 x - 11$ Find: $((g \circ f)) (x)$
49265	Solve the Function Operation	Given f(x)=-x-4 ; find f(4)	Given $f (x) = - x - 4$ ; find $f (4)$
49266	Find the Domain	g(t)=sin(e^t-4)	$g (t) = \sin (e^{t} - 4)$
49267	Find the Slope	(4,-7) and (2,-7)	$(4, - 7)$ and $(2, - 7)$
49268	Solve the Function Operation	Given f(x)=5x+1 ; find f(-3)	Given $f (x) = 5 x + 1$ ; find $f (- 3)$
49269	Find the Domain	y=(x^2+2)/(x^3-x)	$y = \frac{x^{2} + 2}{x^{3} - x}$
49270	Solve the Function Operation	cos(theta)=-12/13 , theta in Quadrant III	$\cos (θ) = - \frac{12}{13}$ , $θ$ in Quadrant $I \cdot I \cdot I$
49271	Find the Domain	f(x)=( natural log of x+1)/(x-2)	$f (x) = \frac{\ln (x + 1)}{x - 2}$
49272	Solve the Function Operation	g(x)=-x^2-1-2x f(x)=x+5 Find (g-f)(x)	$g (x) = - x^{2} - 1 - 2 x$ $f (x) = x + 5$ Find $(g - f) (x)$
49273	Solve the Function Operation	f(x)=x/(1+x) , f(f(x))	$f (x) = \frac{x}{1 + x}$ , $f (f (x))$
49274	Find the Domain	(a-4)/(4a-8)+1/(2a-4)	$\frac{a - 4}{4 a - 8} + \frac{1}{2 a - 4}$
49275	Solve the Function Operation	f(x)=-2x+2 g(x)=x^2-5x+10 Find: g(f(x))	$f (x) = - 2 x + 2$ $g (x) = x^{2} - 5 x + 10$ Find: $g (f (x))$
49276	Find the Slope	(-3,3) and (-9,5)	$(- 3, 3)$ and $(- 9, 5)$
49277	Solve the Function Operation	f(x)=x-3 ; calcula (f(-6))/(f(6))	$f (x) = x - 3$ ; calcula $\frac{f (- 6)}{f (6)}$
49278	Find the Domain	(x^2)/(x^2-16)+(8(x-2))/(16-x^2)	$\frac{x^{2}}{x^{2} - 16} + \frac{8 (x - 2)}{16 - x^{2}}$
49279	Solve the Function Operation	What is (f-g)(x) if f(x)=10x+4 and g(x)=7x+4 ?	What is $(f - g) (x)$ if $f (x) = 10 x + 4$ and $g (x) = 7 x + 4$ ?
49280	Find the Domain	R(x)=(x^2-25)/(x^4-16)	$R (x) = \frac{x^{2} - 25}{x^{4} - 16}$
49281	Find the Slope	(-5,7) and (3,-1)	$(- 5, 7)$ and $(3, - 1)$
49282	Solve the Function Operation	f(x)=10x^(1/3) ; find f^-1(x)	$f (x) = 10 x^{\frac{1}{3}}$ ; find $f^{- 1} (x)$
49283	Solve the Function Operation	f(x)=3x+5 g(x)=4x^2-2 h(x)=x^2-3x+1 Find f(x)+g(x)-h(x)	$f (x) = 3 x + 5$ $g (x) = 4 x^{2} - 2$ $h (x) = x^{2} - 3 x + 1$ Find $f (x) + g (x) - h (x)$
49284	Solve the Function Operation	Find (g*h)(x) if g(x)=x^2+4x+9 and h(x)=x^2-5x+10	Find $(g \cdot h) (x)$ if $g (x) = x^{2} + 4 x + 9$ and $h (x) = x^{2} - 5 x + 10$
49285	Find the Domain	f(x) = square root of 16+6x-x^2	$f (x) = \sqrt{16 + 6 x - x^{2}}$
49286	Find the Domain	d(y)=y+3	$d (y) = y + 3$
49287	Find the Domain	h(x) = square root of x^2-7x+10	$h (x) = \sqrt{x^{2}} - 7 x + 10$
49288	Solve the Function Operation	f(x)=-x-4 ; find f(4)	$f (x) = - x - 4$ ; find $f (4)$
49289	Find the Domain	(7b-14b^2)/(42b^2-21b)	$\frac{7 b - 14 b^{2}}{42 b^{2} - 21 b}$
49290	Solve the Function Operation	f(x)=6(x-9) ; find f^-1(x)	$f (x) = 6 (x - 9)$ ; find $f^{- 1} (x)$
49291	Solve the Function Operation	If f(x)=2x and g(x)=2x^2-1 find g(f(-1))	If $f (x) = 2 x$ and $g (x) = 2 x^{2} - 1$ find $g (f (- 1))$
49292	Find the Asymptotes	tan(pi/2x)	$\tan (\frac{π}{2} x)$
49293	Find the Domain	1/(\|x\|+3)	$\frac{1}{\| x \| + 3}$
49294	Solve the Function Operation	f(x)=(x+3)^2-3 if x<-3; -1 if x=-3; -x-7 if x>-3 Find f(-4)	$f (x) = {\begin{cases} {(x + 3)}^{2} - 3 & x < - 3 \\ - 1 & x = - 3 \\ - x - 7 & x > - 3 \end{cases}$ Find $f (- 4)$
49295	Find the Slope	(-8,-2) and (-4,6)	$(- 8, - 2)$ and $(- 4, 6)$
49296	Find the GCF	18 and 27	$18$ and $27$
49297	Solve the Function Operation	f(x)=(x+3)^2+5 if x<-2; 6 if -2<=x<=2; 2x+2 if x>2 Find f(-1)	$f (x) = {\begin{cases} {(x + 3)}^{2} + 5 & x < - 2 \\ 6 & - 2 \leq x \leq 2 \\ 2 x + 2 & x > 2 \end{cases}$ Find $f (- 1)$
49298	Find the Asymptotes	y=(x^2+7x+12)/(x^2-4)	$y = \frac{x^{2} + 7 x + 12}{x^{2} - 4}$
49299	Find the Average Rate of Change	f(x)=-x^3+24x^2-179x+495	$f (x) = - x^{3} + 24 x^{2} - 179 x + 495$
49300	Solve the Function Operation	f(x) = square root of x+10 ; find f^-1(x)	$f (x) = \sqrt{x} + 10$ ; find $f^{- 1} (x)$