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頻出問題

ランク	トピック	問題	フォーマット化された問題
49901	最大公約数を求める	25x^2+40x+16 and 25x^2-16	$25 x^{2} + 40 x + 16$ and $25 x^{2} - 16$
49902	関数演算を解く	g(x)=-x+2 ; find g(5)	$g (x) = - x + 2$ ; find $g (5)$
49903	傾きを求める	Find the slope of the line passing through the points (-4,6) and (3,-8)	Find the slope of the line passing through the points $(- 4, 6)$ and $(3, - 8)$
49904	頂点を求める	Y=\|x-1\|+3	$Y = \| x - 1 \| + 3$
49905	関数演算を解く	Given that f(x)=x^2+17x+72 and g(x)=x+8 ; find (f-g)(x) and express the result in standard form.	Given that $f (x) = x^{2} + 17 x + 72$ and $g (x) = x + 8$ ; find $(f - g) (x)$ and express the result in standard form.
49906	楕円であるかどうかを証明しなさい。	(x^2)/25+(y^2)/16=1	$\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1$
49907	関数演算を解く	Given that f(x)=x^2+15x+50 and g(x)=x+5 ; find (f(x))÷(g(x)) and express the result in standard form.	Given that $f (x) = x^{2} + 15 x + 50$ and $g (x) = x + 5$ ; find $f (x) \div g (x)$ and express the result in standard form.
49908	関数演算を解く	Given that f(x)=x^2-3x-10 and g(x)=x-5 ; find (f-g)(x) and express the result in standard form.	Given that $f (x) = x^{2} - 3 x - 10$ and $g (x) = x - 5$ ; find $(f - g) (x)$ and express the result in standard form.
49909	定義域を求める	g(s) = square root of (3x+4)/(x^2-5)	$g (s) = \sqrt{\frac{3 x + 4}{x^{2} - 5}}$
49910	関数演算を解く	Given that f(x)=x^2+2x-8 and g(x)=x+4 ; find f(x)*g(x) and express the result in standard form.	Given that $f (x) = x^{2} + 2 x - 8$ and $g (x) = x + 4$ ; find $f (x) \cdot g (x)$ and express the result in standard form.
49911	頂点を求める	y=1/3(x-4)^2	$y = \frac{1}{3} {(x - 4)}^{2}$
49912	関数演算を解く	f(x)=(x+9)^5 ; find f^-1(x)	$f (x) = {(x + 9)}^{5}$ ; find $f^{- 1} (x)$
49913	関数演算を解く	f(x)=(x+4)^(1/3) ; find f^-1(x)	$f (x) = {(x + 4)}^{\frac{1}{3}}$ ; find $f^{- 1} (x)$
49914	関数演算を解く	f(x)=(x-3)^2-2 if x!=3; 2 if x=3 Find f(3)	$f (x) = {\begin{cases} {(x - 3)}^{2} - 2 & x \neq 3 \\ 2 & x = 3 \end{cases}$ Find $f (3)$
49915	関数演算を解く	f(x)＝x+6 ; find f^-1(x)の4乗根	$f (x) = \sqrt[4]{x + 6}$ ; find $f^{- 1} (x)$
49916	定義域を求める	f(x)=( x-2)/(x(x-1))の平方根	$f (x) = \frac{\sqrt{x - 2}}{x (x - 1)}$
49917	漸近線を求める	((x+4)(x+6))/(2x(x+4))	$\frac{(x + 4) (x + 6)}{2 x (x + 4)}$
49918	定義域を求める	1/(\|x\|)	$\frac{1}{\| x \|}$
49919	頂点を求める	2y^2=x-8	$2 y^{2} = x - 8$
49920	最大公約数を求める	x^2-9 and x^2-5x+6	$x^{2} - 9$ and $x^{2} - 5 x + 6$
49921	定義域を求める	3x-6+1の平方根	$\sqrt{3 x - 6} + 1$
49922	傾きを求める	(2,-9) and (8,-9)	$(2, - 9)$ and $(8, - 9)$
49923	定義域を求める	(a^2-b^2)/(a^2-a+ab-b)	$\frac{a^{2} - b^{2}}{a^{2} - a + a b - b}$
49924	傾きを求める	(5/8,-1) and (-1/4,-1/4)	$(\frac{5}{8}, - 1)$ and $(- \frac{1}{4}, - \frac{1}{4})$
49925	変化定数を求める	y=12 when x=4	$y = 12$ when $x = 4$
49926	最大公約数を求める	30 and 42	$30$ and $42$
49927	値域を求める	x^2-4x-5=0	$x^{2} - 4 x - 5 = 0$
49928	定義域を求める	(2-x)^2+3	${(2 - x)}^{2} + 3$
49929	奇関数、偶関数、どちらでもないかを判断する	f(x)=\|x+1\|+\|x-1\|	$f (x) = \| x + 1 \| + \| x - 1 \|$
49930	定義域を求める	(a+10)/(a(a-1))-1	$\frac{a + 10}{a (a - 1)} - 1$
49931	漸近線を求める	((x+8)(x+5))/(3(x+5))	$\frac{(x + 8) (x + 5)}{3 (x + 5)}$
49932	関数演算を解く	f(6) if f(x)=4x	$f (6)$ if $f (x) = 4 x$
49933	定義域を求める	((x+5)/(x^2-5x)-x/(x^2-25))*(x^2-25)/5	$(\frac{x + 5}{x^{2} - 5 x} - \frac{x}{x^{2} - 25}) \cdot \frac{x^{2} - 25}{5}$
49934	定義域を求める	5^(x+1)-20=xの対数の底5	$\log_{5} (5^{x + 1} - 20) = x$
49935	漸近線を求める	f(x)=(3x^3+2x^2)/(x^2+x)	$f (x) = \frac{3 x^{3} + 2 x^{2}}{x^{2} + x}$
49936	関数演算を解く	Let f(x)=3x+2 and g(x)=6x-7 Find f(x)-g(x)	Let $f (x) = 3 x + 2$ and $g (x) = 6 x - 7$ Find $f (x) - g (x)$
49937	関数演算を解く	Given that f(x)=x^2+4x-45 and g(x)=x+9 ; find (f(x))÷(g(x)) and express the result in standard form.	Given that $f (x) = x^{2} + 4 x - 45$ and $g (x) = x + 9$ ; find $f (x) \div g (x)$ and express the result in standard form.
49938	傾きを求める	(-9,-8) and (-15,-16)	$(- 9, - 8)$ and $(- 15, - 16)$
49939	漸近線を求める	f(x)=(2x^3+x^2-3)/(x^2+1)	$f (x) = \frac{2 x^{3} + x^{2} - 3}{x^{2} + 1}$
49940	関数演算を解く	f(x)=4x+2 ; find f(x+3)	$f (x) = 4 x + 2$ ; find $f (x + 3)$
49941	関数の値を求める	3x+y=0 , x>=0	$3 x + y = 0$ , $x \geq 0$
49942	関数演算を解く	f(x)=2x-6 if 0<=x<5; -1 if x=5; -(x-6)^2 if x>5 Find f(5)	$f (x) = {\begin{cases} 2 x - 6 & 0 \leq x < 5 \\ - 1 & x = 5 \\ - {(x - 6)}^{2} & x > 5 \end{cases}$ Find $f (5)$
49943	定義域を求める	( x^2-81)/((x+12)(x-4))の平方根	$\frac{\sqrt{x^{2} - 81}}{(x + 12) (x - 4)}$
49944	関数演算を解く	Given that f(x)=x^2+11x+18 and g(x)=x+2 ; find f(x)-g(x) and express the result in standard form.	Given that $f (x) = x^{2} + 11 x + 18$ and $g (x) = x + 2$ ; find $f (x) - g (x)$ and express the result in standard form.
49945	関数演算を解く	g(x)=-2x+1 ; find g(-1)	$g (x) = - 2 x + 1$ ; find $g (- 1)$
49946	関数演算を解く	If P(x)=x^2+x+4 ; find P(7)	If $P (x) = x^{2} + x + 4$ ; find $P (7)$
49947	傾きを求める	(1,1) and (1,9)	$(1, 1)$ and $(1, 9)$
49948	漸近線を求める	f(x)=2tan(x)	$f (x) = 2 \tan (x)$
49949	最大公約数を求める	28 and 40	$28$ and $40$
49950	関数演算を解く	f(x)=(x+8)^(1/5) ; find f^-1(x)	$f (x) = {(x + 8)}^{\frac{1}{5}}$ ; find $f^{- 1} (x)$
49951	漸近線を求める	(x^2-16)/(x^2+4x)	$\frac{x^{2} - 16}{x^{2} + 4 x}$
49952	漸近線を求める	f(x)=(ax^2+bx+c)/(dx^2+ex+f)	$f (x) = \frac{a x^{2} + b x + c}{d x^{2} + e x + f}$
49953	関数演算を解く	f(x)=2x-1 , g(x)=3x find f(g(-3))	$f (x) = 2 x - 1$ , $g (x) = 3 x$ find $f (g (- 3))$
49954	定義域を求める	x^2-x+2の自然対数＝4の自然対数	$\ln (x^{2} - x + 2) = \ln (4)$
49955	関数演算を解く	f(x)=5x^3+5 ; find f^-1(x)	$f (x) = 5 x^{3} + 5$ ; find $f^{- 1} (x)$
49956	頂点を求める	x^2+2y=8x-7	$x^{2} + 2 y = 8 x - 7$
49957	関数演算を解く	Given that f(x)=x^2-17x+70 and g(x)=x-10 ; find f(x)+g(x) and express the result in standard form.	Given that $f (x) = x^{2} - 17 x + 70$ and $g (x) = x - 10$ ; find $f (x) + g (x)$ and express the result in standard form.
49958	関数演算を解く	f(x)=4x ; find f(-15)	$f (x) = 4 x$ ; find $f (- 15)$
49959	漸近線を求める	(2(3x+8)(3x-8))/(3(x+2)(x-2))	$\frac{2 (3 x + 8) (3 x - 8)}{3 (x + 2) (x - 2)}$
49960	傾きを求める	(-4,10) and (8,-2)	$(- 4, 10)$ and $(8, - 2)$
49961	無限等比級数の和を求める	90+30+10+10/3+...	$90 + 30 + 10 + \frac{10}{3} + \dots$
49962	有理根テストを用いてすべての可能な根を求める	x^3+4x^2+x-6=0	$x^{3} + 4 x^{2} + x - 6 = 0$
49963	関数演算を解く	((9-43/8)[4 5/12-4÷2 2/3+(0,3-0,5÷4),4/7])/(1/24+0,25÷13 1/3)	$\frac{(9 - \frac{43}{8}) [4 \frac{5}{12} - 4 \div 2 \frac{2}{3} + (0, 3 - 0, 5 \div 4), \frac{4}{7}]}{\frac{1}{24} + 0, 25 \div 13 \frac{1}{3}}$
49964	最大公約数を求める	7x and 14xy	$7 x$ and $14 x y$
49965	関数演算を解く	f(x)=-4 if x!=3; 4 if x=3 Find f(3)	$f (x) = {\begin{cases} - 4 & x \neq 3 \\ 4 & x = 3 \end{cases}$ Find $f (3)$
49966	数列の和を求める	22+27+32+37+42+47	$22 + 27 + 32 + 37 + 42 + 47$
49967	傾きを求める	(-4,3) and (-4,-7)	$(- 4, 3)$ and $(- 4, - 7)$
49968	漸近線を求める	(3x^2+27x+54)/(x^2-10x)	$\frac{3 x^{2} + 27 x + 54}{x^{2} - 10 x}$
49969	漸近線を求める	((3x-7)(x+2))/(3(x-10)(x+2))	$\frac{(3 x - 7) (x + 2)}{3 (x - 10) (x + 2)}$
49970	関数演算を解く	g(x)=4x+4 ; find g(4)	$g (x) = 4 x + 4$ ; find $g (4)$
49971	定義域を求める	x-1+の平方根x-2の平方根＝x-3の平方根	$\sqrt{x - 1} + \sqrt{x - 2} = \sqrt{x - 3}$
49972	関数演算を解く	f(x)=(x-2)^2-2 if x<4; 6 if x=4; x-3 if x>4 Find f(4)	$f (x) = {\begin{cases} {(x - 2)}^{2} - 2 & x < 4 \\ 6 & x = 4 \\ x - 3 & x > 4 \end{cases}$ Find $f (4)$
49973	関数演算を解く	Given f(x)=6x+2 ; find f(x+3)	Given $f (x) = 6 x + 2$ ; find $f (x + 3)$
49974	関数演算を解く	f(x)=2x^(1/5)-2 ; find f^-1(x)	$f (x) = 2 x^{\frac{1}{5}} - 2$ ; find $f^{- 1} (x)$
49975	関数演算を解く	Given that f(x)=x^2+9x+18 and g(x)=x+6 ; find f(x)-g(x) and express the result in standard form.	Given that $f (x) = x^{2} + 9 x + 18$ and $g (x) = x + 6$ ; find $f (x) - g (x)$ and express the result in standard form.
49976	関数演算を解く	f(x)=(x+3)^2-6 if x!=-1; 2 if x=-1 Find f(-1)	$f (x) = {\begin{cases} {(x + 3)}^{2} - 6 & x \neq - 1 \\ 2 & x = - 1 \end{cases}$ Find $f (- 1)$
49977	関数演算を解く	Given that f(x)=x^2+4x-21 and g(x)=x-3 ; find (f÷g)(x) and express the result in standard form.	Given that $f (x) = x^{2} + 4 x - 21$ and $g (x) = x - 3$ ; find $(f \div g) (x)$ and express the result in standard form.
49978	漸近線を求める	f(x)=-14/(3x)+5	$f (x) = - \frac{14}{3 x} + 5$
49979	漸近線を求める	y=5+1/(x+3)	$y = 5 + \frac{1}{x + 3}$
49980	傾きを求める	(11/6,-1/2) and (1/3,1/3)	$(\frac{11}{6}, - \frac{1}{2})$ and $(\frac{1}{3}, \frac{1}{3})$
49981	関数演算を解く	g(x)=x-3 f(x)=-2x+2 Find g(f(x))	$g (x) = x - 3$ $f (x) = - 2 x + 2$ Find $g (f (x))$
49982	関数演算を解く	Given that f(x)=x^2-10x+24 and g(x)=x-4 ; find f(x)-g(x) and express the result in standard form.	Given that $f (x) = x^{2} - 10 x + 24$ and $g (x) = x - 4$ ; find $f (x) - g (x)$ and express the result in standard form.
49983	定義域を求める	-(c-b)/(a(3a-c))	$- \frac{c - b}{a (3 a - c)}$
49984	定義域を求める	(5+2x)/(x^2+x+1)	$\frac{5 + 2 x}{x^{2} + x + 1}$
49985	関数演算を解く	If f(x)=x^2 and g(x)=3x-1 ; find f(g(x))	If $f (x) = x^{2}$ and $g (x) = 3 x - 1$ ; find $f (g (x))$
49986	関数演算を解く	h(x)=5x+2 ; find h(-6)	$h (x) = 5 x + 2$ ; find $h (- 6)$
49987	関数演算を解く	h(x)=-3x+1 g(x)=4x+3 Find h(g(x))	$h (x) = - 3 x + 1$ $g (x) = 4 x + 3$ Find $h (g (x))$
49988	関数演算を解く	let f(x)=5x^2+15x-16 and find f(-4)	let $f (x) = 5 x^{2} + 15 x - 16$ and find $f (- 4)$
49989	定義域を求める	(3(3y+2x))/(2x(y+5))	$\frac{3 (3 y + 2 x)}{2 x (y + 5)}$
49990	傾きを求める	(-3,14) and (-2,9)	$(- 3, 14)$ and $(- 2, 9)$
49991	関数演算を解く	f(x)=-(x-7)^2 if x!=5; -3 if x=5 Find f(5)	$f (x) = {\begin{cases} - {(x - 7)}^{2} & x \neq 5 \\ - 3 & x = 5 \end{cases}$ Find $f (5)$
49992	関数演算を解く	Given that f(x)=x^2-3x-18 and g(x)=x-6 ; find f(x)+g(x) and express the result in standard form.	Given that $f (x) = x^{2} - 3 x - 18$ and $g (x) = x - 6$ ; find $f (x) + g (x)$ and express the result in standard form.
49993	傾きを求める	(-8,1) and (-4,-9)	$(- 8, 1)$ and $(- 4, - 9)$
49994	定義域を求める	(cos(x))/(1-sin(x))	$\frac{\cos (x)}{1 - \sin (x)}$
49995	漸近線を求める	(3(x-1)(x+1))/(2(x-1))	$\frac{3 (x - 1) (x + 1)}{2 (x - 1)}$
49996	関数演算を解く	f(x)=7x^(1/5)+6 ; find f^-1(x)	$f (x) = 7 x^{\frac{1}{5}} + 6$ ; find $f^{- 1} (x)$
49997	傾きを求める	(-5,-8) and (5,2)	$(- 5, - 8)$ and $(5, 2)$
49998	傾きを求める	What is the slope of the line through (-4,2) and (3,-3) ?	What is the slope of the line through $(- 4, 2)$ and $(3, - 3)$ ?
49999	最大公約数を求める	Find the GCF of 8r and 14	Find the GCF of $8 r$ and $14$
50000	漸近線を求める	(3(2x-9))/(5x-3)	$\frac{3 (2 x - 9)}{5 x - 3}$