Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
50401	Solve the Function Operation	g(x)=4x+3 f(x)=x^2-1 Find (g-f)(8)	$g (x) = 4 x + 3$ $f (x) = x^{2} - 1$ Find $(g - f) (8)$
50402	Solve the Function Operation	Given that f(x)=x^2-9x+20 and g(x)=x-5 ; find f(x)*g(x) and express the result in standard form.	Given that $f (x) = x^{2} - 9 x + 20$ and $g (x) = x - 5$ ; find $f (x) \cdot g (x)$ and express the result in standard form.
50403	Find the Slope	(3/8,-1/2) , (1/4,1/4)	$(\frac{3}{8}, - \frac{1}{2})$ , $(\frac{1}{4}, \frac{1}{4})$
50404	Find the Asymptotes	f(x)=(3e^(2x)+2)/(e^(2x)-5e^x+6)	$f (x) = \frac{3 e^{2 x} + 2}{e^{2 x} - 5 e^{x} + 6}$
50405	Find the Asymptotes	(2x^3+2x)/(x^2-1)	$\frac{2 x^{3} + 2 x}{x^{2} - 1}$
50406	Find the Asymptotes	f(x)=((x-2)(x-10)(x-5))/(-4x^3-10x^2-9x-2)	$f (x) = \frac{(x - 2) (x - 10) (x - 5)}{- 4 x^{3} - 10 x^{2} - 9 x - 2}$
50407	Find the Asymptotes	(2x(x-8))/(3(x-8))	$\frac{2 x (x - 8)}{3 (x - 8)}$
50408	Solve the Function Operation	f(x)=(x^7)/8+8 ; find f^-1(x)	$f (x) = \frac{x^{7}}{8} + 8$ ; find $f^{- 1} (x)$
50409	Find the Domain	f(x)=-5 fourth root of x , g(x)=19 fourth root of x , x=16	$f (x) = - 5 \sqrt[4]{x}$ , $g (x) = 19 \sqrt[4]{x}$ , $x = 16$
50410	Find the Average Rate of Change	table[[x,y],[-2,3],[-1,5],[0,7],[1,9],[2,11]]	$\begin{array}{c} x & y \\ - 2 & 3 \\ - 1 & 5 \\ 0 & 7 \\ 1 & 9 \\ 2 & 11 \end{array}$
50411	Find the Domain	((m^2-3m)/(8x^2))÷((3m)/(8x))	$\frac{m^{2} - 3 m}{8 x^{2}} \div \frac{3 m}{8 x}$
50412	Find the Domain	(4x)/(9x^(1/2))	$\frac{4 x}{9 x^{\frac{1}{2}}}$
50413	Find the Asymptotes	y=((x-7)(x+10))/((x+10)(x-3)(x-7))	$y = \frac{(x - 7) (x + 10)}{(x + 10) (x - 3) (x - 7)}$
50414	Find the Domain	(2x-1)^(5/3)	${(2 x - 1)}^{\frac{5}{3}}$
50415	Determine if Odd, Even, or Neither	Y=x^2+3x+9	$Y = x^{2} + 3 x + 9$
50416	Solve the Function Operation	If f(x)=3x+7 and g(x)=11x-5 ; find: (f-g)(x)	If $f (x) = 3 x + 7$ and $g (x) = 11 x - 5$ ; find: $(f - g) (x)$
50417	Solve the Function Operation	If f(x)=3x+7 and g(x)=11x-5 ; find: (fg)(x)	If $f (x) = 3 x + 7$ and $g (x) = 11 x - 5$ ; find: $(f g) (x)$
50418	Find the Domain	(t(t-3))/(t-2)+(4-t)/(t-2)	$\frac{t (t - 3)}{t - 2} + \frac{4 - t}{t - 2}$
50419	Find the Domain	k(x) = fifth root of 6+x	$k (x) = \sqrt[5]{6 + x}$
50420	Find the Asymptotes	f(x)=(x^3-6x^2+8x)/(x^2-2x-15)	$f (x) = \frac{x^{3} - 6 x^{2} + 8 x}{x^{2} - 2 x - 15}$
50421	Find the Vertex	f(x)=-2(x^2-4)	$f (x) = - 2 (x^{2} - 4)$
50422	Find the Slope	(-9,-9) and (-6,-12)	$(- 9, - 9)$ and $(- 6, - 12)$
50423	Solve the Function Operation	h(n)=2n-4 g(n)=n-2 Find h(n)+g(n)	$h (n) = 2 n - 4$ $g (n) = n - 2$ Find $h (n) + g (n)$
50424	Find the Domain	y=- square root of -3x	$y = - \sqrt{- 3 x}$
50425	Solve the Function Operation	If f(x)=3x+7 and g(x)=11x-5 ; find: (f+g)(x)	If $f (x) = 3 x + 7$ and $g (x) = 11 x - 5$ ; find: $(f + g) (x)$
50426	Find the Slope	(-3,-2) and (6,-5)	$(- 3, - 2)$ and $(6, - 5)$
50427	Solve the Function Operation	If f(x)=3-2x and g(x)=1/(x+5) ; what is the value of (f/g)(8) ?	If $f (x) = 3 - 2 x$ and $g (x) = \frac{1}{x + 5}$ ; what is the value of $(\frac{f}{g}) (8)$ ?
50428	Find the Slope	(7/6,-1/2) and (1/3,1/3)	$(\frac{7}{6}, - \frac{1}{2})$ and $(\frac{1}{3}, \frac{1}{3})$
50429	Solve the Function Operation	f(x)=6x+2 ; find f(x+3)	$f (x) = 6 x + 2$ ; find $f (x + 3)$
50430	Find the Vertex	4x-y^2-2y-33=0	$4 x - y^{2} - 2 y - 33 = 0$
50431	Find the Slope	(5,-2) and (5,8)	$(5, - 2)$ and $(5, 8)$
50432	Solve the Function Operation	g(a)=4a+1 h(a)=-3a+2 Find g(h(1))	$g (a) = 4 a + 1$ $h (a) = - 3 a + 2$ Find $g (h (1))$
50433	Find the Domain	(4y^2)/(9x^4)	$\frac{4 y^{2}}{9 x^{4}}$
50434	Find the Slope	(-6,-7) and (-24,-7)	$(- 6, - 7)$ and $(- 24, - 7)$
50435	Solve the Function Operation	Given that f(x)=x^2-15x+54 and g(x)=x-6 ; find f(x)*g(x) and express the result in standard form.	Given that $f (x) = x^{2} - 15 x + 54$ and $g (x) = x - 6$ ; find $f (x) \cdot g (x)$ and express the result in standard form.
50436	Solve the Function Operation	f(x)=2x+6 if x!=-1; 6 if x=-1 Find f(-1)	$f (x) = {\begin{cases} 2 x + 6 & x \neq - 1 \\ 6 & x = - 1 \end{cases}$ Find $f (- 1)$
50437	Find the Asymptotes	h(x)=(2x^2-5x-3)/(x^3+x^2-9x-9)	$h (x) = \frac{2 x^{2} - 5 x - 3}{x^{3} + x^{2} - 9 x - 9}$
50438	Find the Asymptotes	f(x)=(-2x^4+x^3-2x+1)/(x^3+3x^2)	$f (x) = \frac{- 2 x^{4} + x^{3} - 2 x + 1}{x^{3} + 3 x^{2}}$
50439	Find the Asymptotes	(2(2x+5))/(3(x-7)(x-1))	$\frac{2 (2 x + 5)}{3 (x - 7) (x - 1)}$
50440	Find the Asymptotes	(2(x+3)(x+7))/((x+1)(x+7))	$\frac{2 (x + 3) (x + 7)}{(x + 1) (x + 7)}$
50441	Find the Asymptotes	(3(2x+5)(2x-5))/(3(2x+5))	$\frac{3 (2 x + 5) (2 x - 5)}{3 (2 x + 5)}$
50442	Find the Domain	(x^2+5x+4)/(x^2-13x+40)*(x-8)/(x^2-1)	$\frac{x^{2} + 5 x + 4}{x^{2} - 13 x + 40} \cdot \frac{x - 8}{x^{2} - 1}$
50443	Find the Domain	(m^2-16n^2)÷((3m+12n)/(mn))	$(m^{2} - 16 n^{2}) \div \frac{3 m + 12 n}{m n}$
50444	Find the Domain	q(x)=1/((x+4)(x-2)(x-7))	$q (x) = \frac{1}{(x + 4) (x - 2) (x - 7)}$
50445	Solve the Function Operation	f(x)=(x^(1/3)+10)/3 ; find f^-1(x)	$f (x) = \frac{x^{\frac{1}{3}} + 10}{3}$ ; find $f^{- 1} (x)$
50446	Find the Slope	(19,3) and (20,3)	$(19, 3)$ and $(20, 3)$
50447	Solve the Function Operation	the expression 4j+2w represents the total cost of buying juice cartons (j) and bottles of water (w) What is the total cost if Hamda buys 7 juice cartons and 3 bottles of water?	the expression $4 j + 2 w$ represents the total cost of buying juice cartons $(j)$ and bottles of water $(w)$ What is the total cost if Hamda buys $7$ juice cartons and $3$ bottles of water?
50448	Find the Domain	f(x,y) = square root of y^2-x	$f (x, y) = \sqrt{y^{2} - x}$
50449	Solve the Function Operation	Find the functions f and g if (fog)(x)=2x^3-5	Find the functions $f$ and $g$ if $((f \circ g)) (x) = 2 x^{3} - 5$
50450	Find the Asymptotes	F(x)=(2x^2-3)/(x^2)	$F (x) = \frac{2 x^{2} - 3}{x^{2}}$
50451	Solve the Function Operation	Find (f-g)(2) if f(x)=4x+10 and g(x)=3x-7	Find $(f - g) (2)$ if $f (x) = 4 x + 10$ and $g (x) = 3 x - 7$
50452	Solve the Function Operation	e(x)=376 (e(x+h)-ex)/h	$e (x) = 376$ $\frac{e (x + h) - e x}{h}$
50453	Find the Average Rate of Change	h(t)=sin(4t) , [0,pi/8]	$h (t) = \sin (4 t)$ , $[0, \frac{π}{8}]$
50454	Evaluate the Function	f(x)=(x+9)/(x+4) , (f(x)-f(1))/(x-1)	$f (x) = \frac{x + 9}{x + 4}$ , $\frac{f (x) - f (1)}{x - 1}$
50455	Find the Maximum Number of Real Roots	256/2401	$\frac{256}{2401}$
50456	Solve the Function Operation	If Q(x)=6x^2-1 ; find Q(-9)	If $Q (x) = 6 x^{2} - 1$ ; find $Q (- 9)$
50457	Find the Slope	(-2,4) and (10,-2)	$(- 2, 4)$ and $(10, - 2)$
50458	Find the Asymptotes	f(x)=(2x-8)/(3x^2+x+1)	$f (x) = \frac{2 x - 8}{3 x^{2} + x + 1}$
50459	Solve the Function Operation	Find f(x+h) for f(x)=x^2+2x	Find $f (x + h)$ for $f (x) = x^{2} + 2 x$
50460	Solve the Function Operation	Given that f(x)=x^2-7x+10 and g(x)=x-2 ; find (f(x))÷(g(x)) and express the result in standard form.	Given that $f (x) = x^{2} - 7 x + 10$ and $g (x) = x - 2$ ; find $f (x) \div g (x)$ and express the result in standard form.
50461	Solve the Function Operation	f(2/9) if f(x)=3x+1/3	$f (\frac{2}{9})$ if $f (x) = 3 x + \frac{1}{3}$
50462	Find the Domain	y=1/( square root of 1-x)	$y = \frac{1}{\sqrt{1 - x}}$
50463	Find the Slope	(-5,3) and (-4,9)	$(- 5, 3)$ and $(- 4, 9)$
50464	Find the Domain	G(x)=(7x+\|x\|)/x	$G (x) = \frac{7 x + \| x \|}{x}$
50465	Find the Slope	(1,4) and (6,-1)	$(1, 4)$ and $(6, - 1)$
50466	Solve the Function Operation	f(x)=(x+2)^(1/5) ; find f^-1(x)	$f (x) = {(x + 2)}^{\frac{1}{5}}$ ; find $f^{- 1} (x)$
50467	Find the Average Rate of Change	table[[x,y],[0,2],[1,6],[2,18],[3,54]]	$\begin{array}{c} x & y \\ 0 & 2 \\ 1 & 6 \\ 2 & 18 \\ 3 & 54 \end{array}$
50468	Find the Domain	(3a+12b)/(6ab)	$\frac{3 a + 12 b}{6 a b}$
50469	Find the Slope	(12,4) and (14,-2)	$(12, 4)$ and $(14, - 2)$
50470	Find the Slope	(-7,-7) and (-9,1)	$(- 7, - 7)$ and $(- 9, 1)$
50471	Find the Slope	(-4,7) and (4,3)	$(- 4, 7)$ and $(4, 3)$
50472	Solve the Function Operation	f(x)=7 cube root of x+8 ; find f^-1(x)	$f (x) = 7 \sqrt[3]{x + 8}$ ; find $f^{- 1} (x)$
50473	Find the Domain	50/(4x-12)+(x-4)/(x^2+x-12)=x/2	$\frac{50}{4 x - 12} + \frac{x - 4}{x^{2} + x - 12} = \frac{x}{2}$
50474	Find the Slope	(-3,-5) and (6,-2)	$(- 3, - 5)$ and $(6, - 2)$
50475	Evaluate the Function	g(x) = square root of 3x-1 , g(x+h)	$g (x) = \sqrt{3 x - 1}$ , $g (x + h)$
50476	Find the Domain	a(r)=r+1/(r-1)	$a (r) = r + \frac{1}{r - 1}$
50477	Find the Domain	y=4/( square root of 4-8x-5x^2)	$y = \frac{4}{\sqrt{4 - 8 x - 5 x^{2}}}$
50478	Solve the Function Operation	If g(x)=x^2+6 and f(x)=2x-4 ; find g(f(x))	If $g (x) = x^{2} + 6$ and $f (x) = 2 x - 4$ ; find $g (f (x))$
50479	Solve the Function Operation	If f(x)=6x+10 and g(x)=7x+11 ; what is (g-f)(x) ?	If $f (x) = 6 x + 10$ and $g (x) = 7 x + 11$ ; what is $(g - f) (x)$ ?
50480	Evaluate the Function	Sales of 10 , 0 increase by 65% each yr	Sales of $10$ , $0$ increase by $65 %$ each $year$
50481	Find the Asymptotes	f(x)=(6x^2+1)/(2x^2+9)	$f (x) = \frac{6 x^{2} + 1}{2 x^{2} + 9}$
50482	Find the Vertex	2x-y^2=4y+10	$2 x - y^{2} = 4 y + 10$
50483	Find the Domain	f(x) = square root of (x-2)/(x-1)+ square root of x^2-x-2	$f (x) = \sqrt{\frac{x - 2}{x - 1}} + \sqrt{x^{2} - x - 2}$
50484	Find the Domain	\|3-x\|-\|x-4\|	$\| 3 - x \| - \| x - 4 \|$
50485	Find the Domain	h(z)=z^5+z^-5	$h (z) = z^{5} + z^{- 5}$
50486	Find the Average Rate of Change	f(x)=x^2 on [1,5]	$f (x) = x^{2}$ on $[1, 5]$
50487	Solve the Function Operation	sin(theta)=3/5 with theta in Quadrant II	$\sin (θ) = \frac{3}{5}$ with $θ$ in Quadrant $I \cdot I$
50488	Find the GCF	8x^4y^6z , 2x^3y^5z	$8 x^{4} y^{6} z$ , $2 x^{3} y^{5} z$
50489	Find the Slope	(-a+3,b-3) and (a+3,-b)	$(- a + 3, b - 3)$ and $(a + 3, - b)$
50490	Find the Asymptotes	f(x)=(x^3+x^2-6x)/(4x^2-4x-8)	$f (x) = \frac{x^{3} + x^{2} - 6 x}{4 x^{2} - 4 x - 8}$
50491	Find the Asymptotes	f(x)=-x/((x-2)^2)	$f (x) = - \frac{x}{{(x - 2)}^{2}}$
50492	Find the Domain	(c+6b)/(ac+2bc-6ab-3a^2)+(2b)/(a^2+2ab)-b/(ac-3a^2)	$\frac{(c + 6 b)}{a c + 2 b c - 6 a b - 3 a^{2}} + \frac{2 b}{a^{2} + 2 a b} - \frac{b}{a c - 3 a^{2}}$
50493	Find the Domain	(2x-1)^(8/3)	${(2 x - 1)}^{\frac{8}{3}}$
50494	Find the Asymptotes	(2x^2)/(4x^2-1)	$\frac{2 x^{2}}{4 x^{2} - 1}$
50495	Solve the Function Operation	f(x)=x^3-3x g(x)=-4x+1 Find f(x)*g(x)	$f (x) = x^{3} - 3 x$ $g (x) = - 4 x + 1$ Find $f (x) \cdot g (x)$
50496	Find the Slope	(-9,6) and (-3,2)	$(- 9, 6)$ and $(- 3, 2)$
50497	Determine if Odd, Even, or Neither	f(x)=sinh(x)	$f (x) = \sinh (x)$
50498	Find the Domain	f(x)=(9-x^2)^(3/2)	$f (x) = {(9 - x^{2})}^{\frac{3}{2}}$
50499	Find the Slope	(5,3) and (8,5)	$(5, 3)$ and $(8, 5)$
50500	Find the Slope	(-4,8) and (4,4)	$(- 4, 8)$ and $(4, 4)$