Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
49001	Solve the Function Operation	given f(x)=3x-2 ; find f(-6)	given $f (x) = 3 x - 2$ ; find $f (- 6)$
49002	Find the Domain	(27a^3)÷((18a^4)/(7b^2))	$27 a^{3} \div \frac{18 a^{4}}{7 b^{2}}$
49003	Find the GCF	27cd , 72 cde	$27 c d$ , $72$ cde
49004	Solve the Function Operation	f(x)=2x^2-7x-4 g(x)=2x-4 Find: f(g(x))	$f (x) = 2 x^{2} - 7 x - 4$ $g (x) = 2 x - 4$ Find: $f (g (x))$
49005	Find the Asymptotes	y=(x^2-3x-4)/(3-x^2)	$y = \frac{x^{2} - 3 x - 4}{3 - x^{2}}$
49006	Find the Slope	(7,1) and (-2,3)	$(7, 1)$ and $(- 2, 3)$
49007	Solve the Function Operation	Solve for x and y*3x+2y=16 7x+y=19	Solve for $x$ and $y \cdot 3 x + 2 y = 16$ $7 x + y = 19$
49008	Find the Asymptotes	(x^2-49)/(2x^2-20x+32)	$\frac{x^{2} - 49}{2 x^{2} - 20 x + 32}$
49009	Solve the Function Operation	f(x)=2x-3 g(x)=x^2-4x+7 Find: (fog)(x)	$f (x) = 2 x - 3$ $g (x) = x^{2} - 4 x + 7$ Find: $((f \circ g)) (x)$
49010	Find the Asymptotes	f(x)=-2 log base 3 of 3-x	$f (x) = - 2 \log_{3} (3 - x)$
49011	Solve the Function Operation	g(n)=n+1 f(n)=n^2-n Find g(f(8))	$g (n) = n + 1$ $f (n) = n^{2} - n$ Find $g (f (8))$
49012	Find the Domain	(ax+ay)/(xy^2)*(x^2y)/(3x+3y)	$\frac{a x + a y}{x y^{2}} \cdot \frac{x^{2} y}{3 x + 3 y}$
49013	Find the Domain	sin(x)^3=sin(x)+1	$\sin^{3} (x) = \sin (x) + 1$
49014	Solve the Function Operation	Given g(x)=-x+2 ; find g(5)	Given $g (x) = - x + 2$ ; find $g (5)$
49015	Find the Asymptotes	(2x-16)/(3x^2-11x+6)	$\frac{2 x - 16}{3 x^{2} - 11 x + 6}$
49016	Find the Domain	((b-2)^2)/((2-b)^2)	$\frac{{(b - 2)}^{2}}{{(2 - b)}^{2}}$
49017	Find the Domain	((y^2-5y+4)/(y^2-1))÷((y^2-9)/(y^2+5y+4))	$\frac{y^{2} - 5 y + 4}{y^{2} - 1} \div \frac{y^{2} - 9}{y^{2} + 5 y + 4}$
49018	Solve the Function Operation	f(x)=3x+10 g(x)=x-2 Find g(f(-10))	$f (x) = 3 x + 10$ $g (x) = x - 2$ Find $g (f (- 10))$
49019	Determine if Odd, Even, or Neither	-2/3x^3	$- \frac{2}{3} x^{3}$
49020	Find the Domain	f(X)=3/(x^2-16)	$f (X) = \frac{3}{x^{2} - 16}$
49021	Solve the Function Operation	f(x)=2x-3 g(x)=3x^2+3x+7 Find: f(g(x))	$f (x) = 2 x - 3$ $g (x) = 3 x^{2} + 3 x + 7$ Find: $f (g (x))$
49022	Evaluate the Function	11^(2x)=14 , 641	$11^{2 x} = 14$ , $641$
49023	Find the Domain	V(w)=(60-4w)w^2	$V (w) = (60 - 4 w) w^{2}$
49024	Find the Asymptotes	f(x)=(6-x)/(3x^2+2)	$f (x) = \frac{6 - x}{3 x^{2} + 2}$
49025	Find the Domain	(x^2-xy)/y*(y^2)/x	$\frac{x^{2} - x y}{y} \cdot \frac{y^{2}}{x}$
49026	Find the Slope	Find the slope of the line passing through the points (3,8) and (7,-7)	Find the slope of the line passing through the points $(3, 8)$ and $(7, - 7)$
49027	Find the Domain	y=(x^3-8)/(x^2+x-2)	$y = \frac{x^{3} - 8}{x^{2} + x - 2}$
49028	Find the Domain	f(x,y)=(x^4+y^4)/(xy)	$f (x, y) = \frac{x^{4} + y^{4}}{x y}$
49029	Find the Asymptotes	f(x)=(3/4)^(2(x+1))-5	$f (x) = {(\frac{3}{4})}^{2 (x + 1)} - 5$
49030	Determine if Odd, Even, or Neither	f(x) = log base 5 of x^2	$f (x) = \log_{5} (x^{2})$
49031	Find the Asymptotes	y=(7x^2+1)/(x^2+7)	$y = \frac{7 x^{2} + 1}{x^{2} + 7}$
49032	Solve the Function Operation	f(x)=3x^2+4x-7 g(x)=2x-11 Find: g(f(x))	$f (x) = 3 x^{2} + 4 x - 7$ $g (x) = 2 x - 11$ Find: $g (f (x))$
49033	Solve the Function Operation	f(x)=x^3-7 ; find f^-1(x)	$f (x) = x^{3} - 7$ ; find $f^{- 1} (x)$
49034	Find the Domain	f(x) = square root of 1+ natural log of x	$f (x) = \sqrt{1 + \ln (x)}$
49035	Find the Asymptotes	f(x)=((x+7)(x-3)(x+1))/((x-3)(x-5))	$f (x) = \frac{(x + 7) (x - 3) (x + 1)}{(x - 3) (x - 5)}$
49036	Find the Domain	5/( square root of x-1-3)	$\frac{5}{\sqrt{x - 1} - 3}$
49037	Solve the Function Operation	f(x)=3x-1 g(x)=x^2-x-4 Find: f(g(x))	$f (x) = 3 x - 1$ $g (x) = x^{2} - x - 4$ Find: $f (g (x))$
49038	Find the Domain	(6(x+4))/(x^2-16)	$\frac{6 (x + 4)}{(x^{2} - 16)}$
49039	Find the Slope	(-2,2) and (-5,-4)	$(- 2, 2)$ and $(- 5, - 4)$
49040	Find the Domain	f(x) = square root of (x^2+2)/(x-2)+3	$f (x) = \sqrt{\frac{x^{2} + 2}{x - 2} + 3}$
49041	Find the Asymptotes	f(x)=(x+5)/(x^3+27)	$f (x) = \frac{x + 5}{x^{3} + 27}$
49042	Find the Asymptotes	((x+1)^2)/(x^2-3x-4)	$\frac{{(x + 1)}^{2}}{x^{2} - 3 x - 4}$
49043	Solve the Function Operation	f(x)=x^2+x-1 g(x)=-3x+12 Find: g(f(x))	$f (x) = x^{2} + x - 1$ $g (x) = - 3 x + 12$ Find: $g (f (x))$
49044	Find the Asymptotes	f(x)=((x+3)^2)/((x+3)(x+4))	$f (x) = \frac{{(x + 3)}^{2}}{(x + 3) (x + 4)}$
49045	Find the Domain	((25x^2-4)/(x^2-9))÷((5x-2)/(x+3))	$\frac{25 x^{2} - 4}{x^{2} - 9} \div \frac{5 x - 2}{x + 3}$
49046	Find the Slope	Find the slope of the line passing through the points (2,5) and (8,-4)	Find the slope of the line passing through the points $(2, 5)$ and $(8, - 4)$
49047	Find the Asymptotes	g(x)=4csc(2x)	$g (x) = 4 \csc (2 x)$
49048	Find the Asymptotes	f(x)=(-3x(x-2))/((x-2)(x+2))	$f (x) = \frac{- 3 x (x - 2)}{(x - 2) (x + 2)}$
49049	Find the Domain	g(t)=sin(e^t-2)	$g (t) = \sin (e^{t} - 2)$
49050	Find the Slope	(2,1) and (3,-10)	$(2, 1)$ and $(3, - 10)$
49051	Solve the Function Operation	f(x)=-2x+4 g(x)=2x^2-5x-11 Find: (gof)(x)	$f (x) = - 2 x + 4$ $g (x) = 2 x^{2} - 5 x - 11$ Find: $((g \circ f)) (x)$
49052	Solve the Function Operation	Given that f(x)=x^2-2x-63 and g(x)=x+7 ; find (f-g)(x) and express the result in standard form.	Given that $f (x) = x^{2} - 2 x - 63$ and $g (x) = x + 7$ ; find $(f - g) (x)$ and express the result in standard form.
49053	Find the Domain	log base x of 5-x	$\log_{x} (5 - x)$
49054	Find the Difference Quotient	F(x)=5/(x^2)	$F (x) = \frac{5}{x^{2}}$
49055	Find the Domain	((m^2+m-mn-n)/(m^2+m+mn+n))÷((m^2-m-mn+n)/(m^2-m+mn-n))	$\frac{m^{2} + m - m n - n}{m^{2} + m + m n + n} \div \frac{m^{2} - m - m n + n}{m^{2} - m + m n - n}$
49056	Solve the Function Operation	h(x)=3x+3 g(x)=-4x+1 Find (h+g)(10)	$h (x) = 3 x + 3$ $g (x) = - 4 x + 1$ Find $(h + g) (10)$
49057	Find the Slope	(-6,4) and (-6,12)	$(- 6, 4)$ and $(- 6, 12)$
49058	Evaluate the Function	(1/(5,0))^(-2z)*5 , 0^(-2z+2)=5 , 0	${(\frac{1}{5, 0})}^{- 2 z} \cdot 5$ , $0^{- 2 z + 2} = 5$ , $0$
49059	Evaluate the Function	5^(2x)=15 , 625	$5^{2 x} = 15$ , $625$
49060	Solve the Function Operation	cos(theta)=-5/13 , theta in Quadrant III	$\cos (θ) = - \frac{5}{13}$ , $θ$ in Quadrant $I \cdot I \cdot I$
49061	Solve the Function Operation	f(x)=-3x+9 if 1<=x<5; -3 if x=5; -(x-7)^2 if x>5 Find f(1)	$f (x) = {\begin{cases} - 3 x + 9 & 1 \leq x < 5 \\ - 3 & x = 5 \\ - {(x - 7)}^{2} & x > 5 \end{cases}$ Find $f (1)$
49062	Find the Nth Root of the Given Value	n=3 , a=1000	$n = 3$ , $a = 1000$
49063	Find the Asymptotes	f(x)=2-3/(x^2)	$f (x) = 2 - \frac{3}{x^{2}}$
49064	Solve the Function Operation	f(x)=4x^(1/3) ; find f^-1(x)	$f (x) = 4 x^{\frac{1}{3}}$ ; find $f^{- 1} (x)$
49065	Find the Slope	(4,7) and (1,3)	$(4, 7)$ and $(1, 3)$
49066	Solve the Function Operation	f(x)=(x+6)^2+3 if x<-5; 0 if x=-5; -2x-8 if x>-5 Find f(-7)	$f (x) = {\begin{cases} {(x + 6)}^{2} + 3 & x < - 5 \\ 0 & x = - 5 \\ - 2 x - 8 & x > - 5 \end{cases}$ Find $f (- 7)$
49067	Find the Domain	(x-2)/(x^2+2x+4)-(6x)/(x^3-8)+1/(x-2)	$\frac{x - 2}{x^{2} + 2 x + 4} - \frac{6 x}{x^{3} - 8} + \frac{1}{x - 2}$
49068	Find the GCF	Find the GCF of 7x and 14xy	Find the GCF of $7 x$ and $14 x y$
49069	Find the Asymptotes	g(x)=(3(x^2+1))/(x^2+2x-15)	$g (x) = \frac{3 (x^{2} + 1)}{x^{2} + 2 x - 15}$
49070	Find the Slope	(0,-2) and (-6,4)	$(0, - 2)$ and $(- 6, 4)$
49071	Find the Asymptotes	g(x)=2/(x^2(x-2))	$g (x) = \frac{2}{x^{2} (x - 2)}$
49072	Solve the Function Operation	Rearrange the equation to isolate a (a+b/c)(d-e)=f	Rearrange the equation to isolate $a$ $(a + \frac{b}{c}) (d - e) = f$
49073	Solve the Function Operation	f(x)=2/3x-2 if x<3; 4 if x=3; -(x-4)^2 if x>3 Find f(6)	$f (x) = {\begin{cases} \frac{2}{3} x - 2 & x < 3 \\ 4 & x = 3 \\ - {(x - 4)}^{2} & x > 3 \end{cases}$ Find $f (6)$
49074	Find the Asymptotes	f(x)=((x-1)(x+2)(x-4))/((x+7)(x-5)(x-3))	$f (x) = \frac{(x - 1) (x + 2) (x - 4)}{(x + 7) (x - 5) (x - 3)}$
49075	Solve the Function Operation	f(x)=-4x-10 g(x)=x^2+x+9 Find: f(g(x))	$f (x) = - 4 x - 10$ $g (x) = x^{2} + x + 9$ Find: $f (g (x))$
49076	Find the Asymptotes	f(x)=(2x)/(x^2)	$f (x) = \frac{2 x}{x^{2}}$
49077	Find Where the Mean Value Theorem is Satisfied	f(x)=-2x^3+6x-2 , [-2,2]	$f (x) = - 2 x^{3} + 6 x - 2$ , $[- 2, 2]$
49078	Solve the Function Operation	f(x)=(x-7)^3 ; find f^-1(x)	$f (x) = {(x - 7)}^{3}$ ; find $f^{- 1} (x)$
49079	Solve the Function Operation	Given g(x)=-3x+3 ; find g(-2)	Given $g (x) = - 3 x + 3$ ; find $g (- 2)$
49080	Find the GCF	4y , 12y	$4 y$ , $12 y$
49081	Solve the Function Operation	16-3p=3 2p+5	$16 - 3 p = 3$ $2 p + 5$
49082	Solve the Function Operation	Given f(x)=-x+2 ; find f(6)	Given $f (x) = - x + 2$ ; find $f (6)$
49083	Solve the Function Operation	f(x)=2x+5 g(x)=x^2-5x+15 Find: (fog)(x)	$f (x) = 2 x + 5$ $g (x) = x^{2} - 5 x + 15$ Find: $((f \circ g)) (x)$
49084	Solve the Function Operation	V_x=6 , 0m/syV_y=-8 , 0m/s	$V_{x} = 6$ , $0 \frac{m}{s} y V_{y} = - 8$ , $0 \frac{m}{s}$
49085	Find the Domain	(x^2-1)/(5x^2+5x)	$\frac{x^{2} - 1}{5 x^{2} + 5 x}$
49086	Find the Domain	y=x/(x+1)	$y = \frac{x}{x + 1}$
49087	Solve the Function Operation	f(x)=-x+6 g(x)=2x^2+x+2 Find: (fog)(x)	$f (x) = - x + 6$ $g (x) = 2 x^{2} + x + 2$ Find: $((f \circ g)) (x)$
49088	Find the Domain	(35x^5y)÷((7x^3)/34)	$35 x^{5} y \div \frac{7 x^{3}}{34}$
49089	Solve the Function Operation	Given g(x)=2x+3 ; find g(-3)	Given $g (x) = 2 x + 3$ ; find $g (- 3)$
49090	Evaluate the Function	h(x)=2/3x-1 , h(9)	$h (x) = \frac{2}{3} x - 1$ , $h (9)$
49091	Solve the Function Operation	f(x)=(x+7)^5 ; find f^-1(x)	$f (x) = {(x + 7)}^{5}$ ; find $f^{- 1} (x)$
49092	Solve the Function Operation	Find g(4c) if g(x)=2x^2-3x+8	Find $g (4 c)$ if $g (x) = 2 x^{2} - 3 x + 8$
49093	Find the Domain	(a/(a-b)-(a-b)/(a+b)+(b^2)/(a^2-b^2))*(a-b)/(3ab)	$(\frac{a}{a - b} - \frac{a - b}{a + b} + \frac{b^{2}}{a^{2} - b^{2}}) \cdot \frac{a - b}{3 a b}$
49094	Find the Domain	f(x) = square root of 4/5-2x	$f (x) = \sqrt{\frac{4}{5} - 2 x}$
49095	Solve the Function Operation	Given g(x)=-x-1 ; find g(-4)	Given $g (x) = - x - 1$ ; find $g (- 4)$
49096	Solve the Function Operation	Given f(x)=5x-3 ; find f(-3)	Given $f (x) = 5 x - 3$ ; find $f (- 3)$
49097	Find the GCF	Find the GCF of 12x and 3	Find the GCF of $12 x$ and $3$
49098	Find the Domain	log base 3 of (1+y)^2=2	$\log_{3} ({(1 + y)}^{2}) = 2$
49099	Find the Domain	f(x)=(x+7)/( square root of x^2-64)	$f (x) = \frac{x + 7}{\sqrt{x^{2} - 64}}$
49100	Find the Domain	(2(x-y))/(y(x+y))	$\frac{2 (x - y)}{y (x + y)}$