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일반적인 문제
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대수학
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일반적인 Functions & Graphing 문제
y=ln(x^2+3)
y
=
ln
(
x
2
+
3
)
f(x)=4cos^4(x)
f
(
x
)
=
4
cos
4
(
x
)
f(x)= 1/3 x^3-ln|x|+e^2
f
(
x
)
=
1
3
x
3
−
ln
|
x
|
+
e
2
y=log_{1/3}(x+1)
y
=
log
1
3
(
x
+
1
)
f(x)=\sqrt[3]{x^2-2x+9}
f
(
x
)
=
3
√
x
2
−
2
x
+
9
f(x)=2x+3/(x^2-4)
f
(
x
)
=
2
x
+
3
x
2
−
4
f(x)=-x^2+22x+112
f
(
x
)
=
−
x
2
+
2
2
x
+
1
1
2
y=10+3x-x^2
y
=
1
0
+
3
x
−
x
2
f(x)=-|2x+1|+3
f
(
x
)
=
−
|
2
x
+
1
|
+
3
f(x)=sqrt(x^2+1-x)
f
(
x
)
=
√
x
2
+
1
−
x
y=e^{4x}+6sin(3x)
y
=
e
4
x
+
6
sin
(
3
x
)
f(x)=(6x-1)/(10x+4)
f
(
x
)
=
6
x
−
1
1
0
x
+
4
f(x)=(-2x)/(x+1)
f
(
x
)
=
−
2
x
x
+
1
f(x)=x^{10/3}
f
(
x
)
=
x
1
0
3
f(x)= 1/4 x^4-x^3+x^2
f
(
x
)
=
1
4
x
4
−
x
3
+
x
2
f(x)=(sqrt(2+x)-sqrt(2))/x
f
(
x
)
=
√
2
+
x
−
√
2
x
f(x)=(1-2x+x^2)/4
f
(
x
)
=
1
−
2
x
+
x
2
4
y= 3/(x-3)
y
=
3
x
−
3
f(x)=((4x-3)^3)/((2x-3)^4)
f
(
x
)
=
(
4
x
−
3
)
3
(
2
x
−
3
)
4
y=ln^2(sqrt(x))
y
=
ln
2
(
√
x
)
f(t)=6sin^2(3t)-(t+2)^2+3e^{-2t}
f
(
t
)
=
6
sin
2
(
3
t
)
−
(
t
+
2
)
2
+
3
e
−
2
t
f(x)=(x-3)/(\sqrt[3]{x-3)+1}
f
(
x
)
=
x
−
3
3
√
x
−
3
+
1
f(x)=3^x+4^x
f
(
x
)
=
3
x
+
4
x
f(x)=2x^3-15x^2+36x-2
f
(
x
)
=
2
x
3
−
1
5
x
2
+
3
6
x
−
2
y=e^{600x}
y
=
e
6
0
0
x
f(x)=-3x-15
f
(
x
)
=
−
3
x
−
1
5
f(x)= 2/((5x+1)^3)
f
(
x
)
=
2
(
5
x
+
1
)
3
36y^2=(x^2-4)^3,4<= x<= 9,y>= 0
3
6
y
2
=
(
x
2
−
4
)
3
,
4
≤
x
≤
9
,
y
≥
0
f(x)=-42.784x^2+4078.632x-51062.202
f
(
x
)
=
−
4
2
.
7
8
4
x
2
+
4
0
7
8
.
6
3
2
x
−
5
1
0
6
2
.
2
0
2
y=10x-25-x^2
y
=
1
0
x
−
2
5
−
x
2
f(t)=e^{6t}sin^4(t)
f
(
t
)
=
e
6
t
sin
4
(
t
)
f(x)=-3sqrt(-2x-3)
f
(
x
)
=
−
3
√
−
2
x
−
3
f(t)=-4t^2+16t+9
f
(
t
)
=
−
4
t
2
+
1
6
t
+
9
f(x)=(x^3+8)/x
f
(
x
)
=
x
3
+
8
x
f(x)=sqrt((x^4+4x^3+3x^2)/(x^2+4x+3))
f
(
x
)
=
√
x
4
+
4
x
3
+
3
x
2
x
2
+
4
x
+
3
y=e^x-e
y
=
e
x
−
e
f(x)=-2.2x^2+396x-400
f
(
x
)
=
−
2
.
2
x
2
+
3
9
6
x
−
4
0
0
h(t)=16t^2+16t-sin(3t)
h
(
t
)
=
1
6
t
2
+
1
6
t
−
sin
(
3
t
)
y=(x-1)/(x+4)
y
=
x
−
1
x
+
4
f(x)= 4/(1+3x^3)
f
(
x
)
=
4
1
+
3
x
3
f(x)=2x^3-4x^2+2x+1
f
(
x
)
=
2
x
3
−
4
x
2
+
2
x
+
1
f(x)=2sin(x)+cos(x)
f
(
x
)
=
2
sin
(
x
)
+
cos
(
x
)
f(x)=sin(3x)cos(4x)
f
(
x
)
=
sin
(
3
x
)
cos
(
4
x
)
36y^2=(x^2-4)^3,5<= x<= 9,y>= 0
3
6
y
2
=
(
x
2
−
4
)
3
,
5
≤
x
≤
9
,
y
≥
0
f(x)=-3cos(x-pi/3)
f
(
x
)
=
−
3
cos
(
x
−
π
3
)
f(x)=(x-7)(x-9)
f
(
x
)
=
(
x
−
7
)
(
x
−
9
)
f(x)= 1/((x^4+x^2+1))
f
(
x
)
=
1
(
x
4
+
x
2
+
1
)
f(x)=x*6
f
(
x
)
=
x
·
6
f(x)=(x^2+7x+2)/(sqrt(x+2))
f
(
x
)
=
x
2
+
7
x
+
2
√
x
+
2
f(a)=a^2-a+2
f
(
a
)
=
a
2
−
a
+
2
f(x)=3x^2+x+3
f
(
x
)
=
3
x
2
+
x
+
3
f(x)=-e^{-x}+1
f
(
x
)
=
−
e
−
x
+
1
f(t)=8cos^2(2t)+(t-5)^2-7e^{4t}
f
(
t
)
=
8
cos
2
(
2
t
)
+
(
t
−
5
)
2
−
7
e
4
t
f(x)=(3x)/(2x-3)+4/(3-2x)
f
(
x
)
=
3
x
2
x
−
3
+
4
3
−
2
x
f(x)= x/2-cos(x)
f
(
x
)
=
x
2
−
cos
(
x
)
f(x)=x^2(x+4)^3
f
(
x
)
=
x
2
(
x
+
4
)
3
y= 1/3 cos(x)
y
=
1
3
cos
(
x
)
f(a)=|a-2|
f
(
a
)
=
|
a
−
2
|
y=-1+4x-x^2
y
=
−
1
+
4
x
−
x
2
f(x)=7sin(x)+7cos(x)
f
(
x
)
=
7
sin
(
x
)
+
7
cos
(
x
)
f(x)=ln(x)*2x
f
(
x
)
=
ln
(
x
)
·
2
x
f(x)=|log_{10}(x)|
f
(
x
)
=
|
log
1
0
(
x
)
|
f(t)=(t^4-1)^3(t^3+1)^4
f
(
t
)
=
(
t
4
−
1
)
3
(
t
3
+
1
)
4
f(x)=(2x^2+3x)/(x-1)
f
(
x
)
=
2
x
2
+
3
x
x
−
1
f(x)=3x^2+24x+46
f
(
x
)
=
3
x
2
+
2
4
x
+
4
6
y=-2x^2+6x-4
y
=
−
2
x
2
+
6
x
−
4
g(x)=ln(4-x)
g
(
x
)
=
ln
(
4
−
x
)
f(x)=-sqrt(-x)+3
f
(
x
)
=
−
√
−
x
+
3
f(x)=2x^2-7x-12
f
(
x
)
=
2
x
2
−
7
x
−
1
2
f(x)=(5x-7)/2
f
(
x
)
=
5
x
−
7
2
f(x)=(2/(1-x))/(2+1/(1-x))
f
(
x
)
=
2
1
−
x
2
+
1
1
−
x
f(x)=e^{sqrt(x/2+5)}-30
f
(
x
)
=
e
√
x
2
+
5
−
3
0
f(x)=x^4+4x^2+1
f
(
x
)
=
x
4
+
4
x
2
+
1
f(θ)=(θ-3)cos(θ)
f
(
θ
)
=
(
θ
−
3
)
cos
(
θ
)
f(x)=ln((1-x)/(1+x))
f
(
x
)
=
ln
(
1
−
x
1
+
x
)
y=-3x^2-5x-2
y
=
−
3
x
2
−
5
x
−
2
y=-3*2^{x-5}+5
y
=
−
3
·
2
x
−
5
+
5
f(x)=sqrt(4+3x-x^2)
f
(
x
)
=
√
4
+
3
x
−
x
2
y=(x-3)/3
y
=
x
−
3
3
f(x)=x^3-2x^2-29x+30
f
(
x
)
=
x
3
−
2
x
2
−
2
9
x
+
3
0
y=-3x^2+18x+10
y
=
−
3
x
2
+
1
8
x
+
1
0
y=|x^2+x|-2
y
=
|
x
2
+
x
|
−
2
f(x)=sqrt(6+x)
f
(
x
)
=
√
6
+
x
f(x)=(2x-1)/(-x+2)
f
(
x
)
=
2
x
−
1
−
x
+
2
f(x)=(4x^3-9)^{2/5}
f
(
x
)
=
(
4
x
3
−
9
)
2
5
f(x)=1-2cos(x/3+(2pi)/3)
f
(
x
)
=
1
−
2
cos
(
x
3
+
2
π
3
)
f(x)=sqrt(-x-4)
f
(
x
)
=
√
−
x
−
4
f(x)=(sqrt(x^2-9))/x
f
(
x
)
=
√
x
2
−
9
x
f(x)=9x^2-1
f
(
x
)
=
9
x
2
−
1
y=-4sin(3x-pi)-3
y
=
−
4
sin
(
3
x
−
π
)
−
3
p(x)=-5x^2+500x
p
(
x
)
=
−
5
x
2
+
5
0
0
x
f(x)=x^4-12x^2+3
f
(
x
)
=
x
4
−
1
2
x
2
+
3
f(x)=x^3-3x^2+2x+5
f
(
x
)
=
x
3
−
3
x
2
+
2
x
+
5
f(x)= 1/(sqrt(8x-16))
f
(
x
)
=
1
√
8
x
−
1
6
f(x)=-x^3+x^2-9x+8
f
(
x
)
=
−
x
3
+
x
2
−
9
x
+
8
y=2(5^x)
y
=
2
(
5
x
)
y=x*e^x
y
=
x
·
e
x
f(x)=-log_{5}(x-6)-3
f
(
x
)
=
−
log
5
(
x
−
6
)
−
3
f(x)=2x^2-7x
f
(
x
)
=
2
x
2
−
7
x
f(x)=x^3+x^2+x+2
f
(
x
)
=
x
3
+
x
2
+
x
+
2
1
..
952
953
954
955
956
..
1324