Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
48801	Solve the Function Operation	Given h(x)=4x+3 ; find h(-1)	Given $h (x) = 4 x + 3$ ; find $h (- 1)$
48802	Find the Vertex	Y=x^2+4x	$Y = x^{2} + 4 x$
48803	Find the Domain	(y-1)/(y square root of y+1)	$\frac{y - 1}{y \sqrt{y + 1}}$
48804	Find the Domain	(5x)/( square root of 14-x)	$\frac{5 x}{\sqrt{14 - x}}$
48805	Find the Asymptotes	(y/2)-1=4^(x-1)	$(\frac{y}{2}) - 1 = 4^{x - 1}$
48806	Find the Domain	(b^2-4by)/(2y^2-by)-(4y)/(b-2y)	$\frac{b^{2} - 4 b y}{2 y^{2} - b y} - \frac{4 y}{b - 2 y}$
48807	Find the Domain	square root of 13-(13-2x)	$\sqrt{13 - (13 - 2 x)}$
48808	Find the Domain	(x^2-25)/(x^2-5x)	$\frac{x^{2} - 25}{x^{2} - 5 x}$
48809	Find the Domain	((2a+b)/a-(a+2b)/b)*((a-b)/(b^2+ab)+(a+b)/(b^2-ab))	$(\frac{2 a + b}{a} - \frac{a + 2 b}{b}) \cdot (\frac{a - b}{b^{2} + a b} + \frac{a + b}{b^{2} - a b})$
48810	Find the Domain	((x+5)(x^2-25))/((x+5)^2(x-5)^2)	$\frac{(x + 5) (x^{2} - 25)}{{(x + 5)}^{2} {(x - 5)}^{2}}$
48811	Find the Domain	(y^2+1)/(y^2-2y)	$\frac{y^{2} + 1}{y^{2} - 2 y}$
48812	Find the Asymptotes	f(x)=(7+3e^(3x))/(4-8e^(3x))	$f (x) = \frac{7 + 3 e^{3 x}}{4 - 8 e^{3 x}}$
48813	Find the Domain	(4y)/(3x^2+2xy)-(9x)/(3xy+2y^2)	$\frac{4 y}{3 x^{2} + 2 x y} - \frac{9 x}{3 x y + 2 y^{2}}$
48814	Find the Domain	(ab^2-a^2b)/(ab)*(a^2b^2)/(a-b)	$\frac{a b^{2} - a^{2} b}{a b} \cdot \frac{a^{2} b^{2}}{a - b}$
48815	Find the Domain	(c+6b)/(ac+2bc-6ab-3a^2)+(2b)/(a^2+2ab)-b/(ac-3a^2)	$\frac{c + 6 b}{a c + 2 b c - 6 a b - 3 a^{2}} + \frac{2 b}{a^{2} + 2 a b} - \frac{b}{a c - 3 a^{2}}$
48816	Find the Domain	((x^2-bx+ax-ab)/(x^2+bx-ax-ab))÷((x^2+bx+ax+ab)/(x^2-bx-ax+ab))	$\frac{x^{2} - b x + a x - a b}{x^{2} + b x - a x - a b} \div \frac{x^{2} + b x + a x + a b}{x^{2} - b x - a x + a b}$
48817	Find the Domain	x/(x+1)-(x+1)/(x^2+2x+1)-2/(x^2-1)	$\frac{x}{x + 1} - \frac{x + 1}{x^{2} + 2 x + 1} - \frac{2}{x^{2} - 1}$
48818	Find the Domain	((2ab)/(a^2-b^2))÷((4ab)/((a-b)^2))	$\frac{2 a b}{a^{2} - b^{2}} \div \frac{4 a b}{{(a - b)}^{2}}$
48819	Find the Domain	((a+b)/b-a/(a+b))÷((a+b)/a-b/(a+b))	$(\frac{a + b}{b} - \frac{a}{a + b}) \div (\frac{a + b}{a} - \frac{b}{a + b})$
48820	Find the Domain	log base 1-x of x	$\log_{1 - x} (x)$
48821	Find the Domain	F(x) = square root of x^2+4	$F (x) = \sqrt{x^{2} + 4}$
48822	Find the Vertex	F(x)=(x+1)^2	$F (x) = {(x + 1)}^{2}$
48823	Find the Domain	(2b)/(2b+3)+5/(3-2b)-(4b^2+9)/(4b^2-9)	$\frac{2 b}{2 b + 3} + \frac{5}{3 - 2 b} - \frac{4 b^{2} + 9}{4 b^{2} - 9}$
48824	Find the Domain	(x^2-8)/(4x(x+1))	$\frac{x^{2} - 8}{4 x (x + 1)}$
48825	Find the Asymptotes	f(x)=(X+8)/(6x-15)	$f (x) = \frac{X + 8}{6 x - 15}$
48826	Find the Domain	y=(18-2x)/(x^2-3x)-6/(3-x)	$y = \frac{18 - 2 x}{x^{2} - 3 x} - \frac{6}{3 - x}$
48827	Find the Domain	(9x^2+4y^2-12xy)/(4y^2-9x^2)	$\frac{9 x^{2} + 4 y^{2} - 12 x y}{4 y^{2} - 9 x^{2}}$
48828	Find the Domain	(x-5)/(x^2+25)-3x	$\frac{x - 5}{x^{2} + 25} - 3 x$
48829	Find the Domain	((2a-b)^2)÷((4a^3-ab^2)/3)	${(2 a - b)}^{2} \div \frac{4 a^{3} - a b^{2}}{3}$
48830	Find the Domain	f(x) = log base 1-x of x	$f (x) = \log_{1 - x} (x)$
48831	Find the Domain	(a^2-b^2)/(a^2-3a)*(2a-6)/((a+b)^2)	$\frac{a^{2} - b^{2}}{a^{2} - 3 a} \cdot \frac{2 a - 6}{{(a + b)}^{2}}$
48832	Find the Domain	((x-y)^2)/(2xy+6y)*(4x+12)/(x^2-y^2)	$\frac{{(x - y)}^{2}}{2 x y + 6 y} \cdot \frac{4 x + 12}{x^{2} - y^{2}}$
48833	Find the Domain	(x-5)/(x^2+1)-x^2	$\frac{x - 5}{x^{2} + 1} - x^{2}$
48834	Find the Domain	1/( square root of y)(1/( square root of x- square root of y)-1/( square root of x+ square root of y))	$\frac{1}{\sqrt{y}} (\frac{1}{\sqrt{x} - \sqrt{y}} - \frac{1}{\sqrt{x} + \sqrt{y}})$
48835	Find the Domain	y/(y-6)+15/(y+6)	$\frac{y}{y - 6} + \frac{15}{y + 6}$
48836	Find the Domain	y=1/( square root of x^2-x-2)	$y = \frac{1}{\sqrt{x^{2} - x - 2}}$
48837	Find the Domain	(x-3)/(x^2-64)+11/(x^2-64)	$\frac{x - 3}{x^{2} - 64} + \frac{11}{x^{2} - 64}$
48838	Find the Domain	((a^2-4)/(x^2-9))÷((a^2-2a)/(xy+3y))+(2-y)/(x-3)	$\frac{a^{2} - 4}{x^{2} - 9} \div \frac{a^{2} - 2 a}{x y + 3 y} + \frac{2 - y}{x - 3}$
48839	Find the Domain	(x^2+2x-3)/(2x^2+x-3)	$\frac{x^{2} + 2 x - 3}{2 x^{2} + x - 3}$
48840	Find the Domain	a/(2a-b)+(3a-b)/(b-2a)	$\frac{a}{2 a - b} + \frac{3 a - b}{b - 2 a}$
48841	Find the Domain	(b-c)/(a+b)-(ab-b^2)/(a^2-ac)*(a^2-c^2)/(a^2-b^2)	$\frac{b - c}{a + b} - \frac{a b - b^{2}}{a^{2} - a c} \cdot \frac{a^{2} - c^{2}}{a^{2} - b^{2}}$
48842	Find the Asymptotes	y=((x+1)^2)/(x^2-3x-4)	$y = \frac{{(x + 1)}^{2}}{x^{2} - 3 x - 4}$
48843	Determine if Odd, Even, or Neither	f(x)=1/(x^6+9x^4)	$f (x) = \frac{1}{x^{6} + 9 x^{4}}$
48844	Find the Domain	((2a+3b)/(2a)+(2a-3b)/(3b))^2-((2a+3b)/(2a)-(2a-3b)/(3b))^2	${(\frac{2 a + 3 b}{2 a} + \frac{2 a - 3 b}{3 b})}^{2} - {(\frac{2 a + 3 b}{2 a} - \frac{2 a - 3 b}{3 b})}^{2}$
48845	Find the Domain	(2a+b)/(2a^2-ab)-(16a)/(4a^2-b^2)-(2a-b)/(2a^2+ab)	$\frac{2 a + b}{2 a^{2} - a b} - \frac{16 a}{4 a^{2} - b^{2}} - \frac{2 a - b}{2 a^{2} + a b}$
48846	Find the Asymptotes	y=(1-3x)/(2+x)	$y = \frac{1 - 3 x}{2 + x}$
48847	Find the Nth Root of the Given Value	n=2 , a=36	$n = 2$ , $a = 36$
48848	Find the Domain	(a+3)/(a^2-1)-1/(a^2+a)	$\frac{a + 3}{a^{2} - 1} - \frac{1}{a^{2} + a}$
48849	Solve the Function Operation	(1/(5,0))^(-2z)*5 , 0^(-2z+2)=5 , 0	${(\frac{1}{5, 0})}^{- 2 z} \cdot 5$ , $0^{- 2 z + 2} = 5$ , $0$
48850	Find the Domain	a/(a-b)+(3a)/(a+b)-(2ab)/(a^2-b^2)	$\frac{a}{a - b} + \frac{3 a}{a + b} - \frac{2 a b}{a^{2} - b^{2}}$
48851	Determine if Odd, Even, or Neither	F(x)=x^5-x	$F (x) = x^{5} - x$
48852	Find the Domain	(-1/x)(1-x)/(1+x)x/(x^2-1)	$(- \frac{1}{x}) \cdot \frac{1 - x}{1 + x} \cdot \frac{x}{x^{2} - 1}$
48853	Find the Vertex	4x^2+y^2-36=0	$4 x^{2} + y^{2} - 36 = 0$
48854	Find the Domain	(x-y)/(xy)-(x-z)/(xz)	$\frac{x - y}{x y} - \frac{x - z}{x z}$
48855	Find the Domain	(a-2y)/(a+y)-(y^2-5ay)/(a^2-y^2)	$\frac{a - 2 y}{a + y} - \frac{y^{2} - 5 a y}{a^{2} - y^{2}}$
48856	Find the Domain	(x^2-1)/(5xy)*(x^2y)/(1+x)	$\frac{x^{2} - 1}{5 x y} \cdot \frac{x^{2} y}{1 + x}$
48857	Find the Domain	(4ab)/(cx+dx)*(ax+bx)/(2ab)	$\frac{4 a b}{c x + d x} \cdot \frac{a x + b x}{2 a b}$
48858	Find the Domain	((x^2-9)/(y^2-25))÷((2x^2-6x)/(3y^2-15y))+(3-1.5y)/(y+5)	$\frac{x^{2} - 9}{y^{2} - 25} \div \frac{2 x^{2} - 6 x}{3 y^{2} - 15 y} + \frac{3 - 1.5 y}{y + 5}$
48859	Find the Asymptotes	y=x/(2-3x)	$y = \frac{x}{2 - 3 x}$
48860	Find the Nth Root of the Given Value	n=4 , a=81	$n = 4$ , $a = 81$
48861	Find the Domain	tan(arctan(x))	$\tan (\arctan (x))$
48862	Find the Domain	x/(x+8)+(x-8)/x	$\frac{x}{x + 8} + \frac{x - 8}{x}$
48863	Find the Domain	(x^2-1)/(x^3+2x^2-8x)-( square root of x+1)/(1-x)	$\frac{x^{2} - 1}{x^{3} + 2 x^{2} - 8 x} - \frac{\sqrt{x + 1}}{1 - x}$
48864	Find the Asymptotes	f(x)=3tan(x)	$f (x) = 3 \tan (x)$
48865	Find the Domain	-(35ax^2)/(12b^2)*(8ab)/(21xy)	$- \frac{35 a x^{2}}{12 b^{2}} \cdot \frac{8 a b}{21 x y}$
48866	Find the Asymptotes	A(x)=4^(x-3)+1	$A (x) = 4^{x - 3} + 1$
48867	Find the Domain	(5p)/(2q-p)+(10q)/(p-2q)	$\frac{5 p}{2 q - p} + \frac{10 q}{p - 2 q}$
48868	Find the Vertex	f(x)=(2-x)^2+3	$f (x) = {(2 - x)}^{2} + 3$
48869	Find the Domain	f(x)=1/( square root of 2- square root of x)	$f (x) = \frac{1}{\sqrt{2 - \sqrt{x}}}$
48870	Find the Domain	f(x)=5/( square root of X-4)	$f (x) = \frac{5}{\sqrt{X - 4}}$
48871	Find the Domain	32/y-(y+1)/(y+7)	$\frac{32}{y} - \frac{y + 1}{y + 7}$
48872	Find the Domain	(4y)/(x-3y)+(2x-2y)/(3y-x)	$\frac{4 y}{x - 3 y} + \frac{2 x - 2 y}{3 y - x}$
48873	Find the Vertex	(x-1)^2+8(y+2)=0	${(x - 1)}^{2} + 8 (y + 2) = 0$
48874	Solve the Function Operation	15+18 , 36-75+84 , 214-0 , 25	$15 + 18$ , $36 - 75 + 84$ , $214 - 0$ , $25$
48875	Determine if Odd, Even, or Neither	f(x)=e^(x^4-x)	$f (x) = e^{x^{4} - x}$
48876	Find the Domain	4/(y+2)-3/(y-2)+12/(y^2-4)	$\frac{4}{y + 2} - \frac{3}{y - 2} + \frac{12}{y^{2} - 4}$
48877	Find the Domain	(14/(9x^3))÷((7x)/(2y^2))	$\frac{14}{9 x^{3}} \div \frac{7 x}{2 y^{2}}$
48878	Find the Domain	cube root of x+2- square root of x=2x	$\sqrt[3]{x + 2} - \sqrt{x} = 2 x$
48879	Find the Domain	1/( square root of 2- square root of x)	$\frac{1}{\sqrt{2 - \sqrt{x}}}$
48880	Find the Domain	4^x-14*2^x-32=0	$4^{x} - 14 \cdot 2^{x} - 32 = 0$
48881	Find the Domain	(3a-1)/(a^2-b^2)-(3b-1)/(a^2-b^2)	$\frac{3 a - 1}{a^{2} - b^{2}} - \frac{3 b - 1}{a^{2} - b^{2}}$
48882	Find the Domain	(a-(2a-1)/a)/((1-a)/(3a))	$\frac{a - \frac{2 a - 1}{a}}{\frac{1 - a}{3 a}}$
48883	Find the Domain	1/(\|x\|-3)	$\frac{1}{\| x \| - 3}$
48884	Find the Domain	(-6 plus or minus square root of 6^2-4*1(y^2-2y-15))/2	$\frac{- 6 \pm \sqrt{6^{2} - 4 \cdot 1 (y^{2} - 2 y - 15)}}{2}$
48885	Find the Asymptotes	f(x)=1/2*5^(-x)-1	$f (x) = \frac{1}{2} \cdot 5^{- x} - 1$
48886	Find the Vertex	Y=(x+1)^2-2	$Y = {(x + 1)}^{2} - 2$
48887	Find the Domain	log base 4 of x^2-x=1+ log base 4 of 5	$\log_{4} (x^{2} - x) = 1 + \log_{4} (5)$
48888	Solve the Function Operation	5^(2x)=15 , 625	$5^{2 x} = 15$ , $625$
48889	Find the Domain	(ax-ay)/(5x^2y^2)*(-(5xy)/(by-bx))	$\frac{a x - a y}{5 x^{2} y^{2}} \cdot (- \frac{5 x y}{b y - b x})$
48890	Find the Factors Using the Factor Theorem	x^3-3x+2 , x+2	$x^{3} - 3 x + 2$ , $x + 2$
48891	Determine if Odd, Even, or Neither	f(x)=(x-2)^2(x+3)(x+1)^2	$f (x) = {(x - 2)}^{2} (x + 3) {(x + 1)}^{2}$
48892	Find the Domain	(mx^2-my^2)/(2m+8)*(3m+12)/(my+mx)	$\frac{m x^{2} - m y^{2}}{2 m + 8} \cdot \frac{3 m + 12}{m y + m x}$
48893	Solve the Function Operation	3^(2x)=6 , 561	$3^{2 x} = 6$ , $561$
48894	Find the Domain	x^2- square root of 1+x^2=2/( cube root of x^2-1)	$x^{2} - \sqrt{1 + x^{2}} = \frac{2}{\sqrt[3]{x^{2} - 1}}$
48895	Find the Asymptotes	f(x)=-1/3*6^x+5	$f (x) = - \frac{1}{3} \cdot 6^{x} + 5$
48896	Find the Domain	F(x)=x/(x-3)	$F (x) = \frac{x}{x - 3}$
48897	Determine if Odd, Even, or Neither	f(x)=e^(x^6-x)	$f (x) = e^{x^{6} - x}$
48898	Find the Domain	(3/2a^2-2ab+2/3b^2)/(1/4a^2-1/9b^2)+(6b)/(3/4a+1/2b)	$\frac{\frac{3}{2} a^{2} - 2 a b + \frac{2}{3} b^{2}}{\frac{1}{4} a^{2} - \frac{1}{9} b^{2}} + \frac{6 b}{\frac{3}{4} a + \frac{1}{2} b}$
48899	Find the Domain	(5y+3)/(2y+2)-(7y+4)/(3y+3)	$\frac{5 y + 3}{2 y + 2} - \frac{7 y + 4}{3 y + 3}$
48900	Find the Domain	-(25x^3y^3)/(14a^2b)*(-(21ab)/(10x^2y))	$- \frac{25 x^{3} y^{3}}{14 a^{2} b} \cdot (- \frac{21 a b}{10 x^{2} y})$