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# Inverse Functions (Grades 11-12)

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## Inverse Functions

1.
Find the inverse of $g(x)=-3x$.
1. $g ^(-1) (x)=x+1$
2. $g ^-1 (x)=-3x-3$
3. $g ^-1 (x)=x-1$
4. $g ^-1(x)= -1/3 x$
2.
Which is the inverse of $f(x)=2x-7$?
1. $f^-1(x)=2/7(x+1)$
2. $f^-1(x)=2/7x+7$
3. $f^-1(x)=(x+7)/2$
4. $f^-1(x)=x/2+7$
3.
Which restriction would make the function $y=(x-2)^2+4$ invertible?
1. $y> -2$
2. $x>2$
3. $y<4$
4. $y> -4$
4.
Which restriction would make the function $y=(x+2)^2$ invertible?
1. $y> -2$
2. $x>2$
3. $y<0$
4. $x<-2$
5.
Which restriction would make the function $y=1/2x^2$ invertible?
1. $y> -4$
2. $x>0$
3. $y<0$
4. $x<1/2$
6.
Which of the following is the inverse of $y=x^2+4, x<=0$ ?
1. $-y=sqrt(x-4)$
2. $y=+-sqrt(x)-2$
3. $x=+-sqrt(y^2+4)$
4. $y=sqrt(x)-4$
7.
Which of the following is the inverse of $y=(5x^2+4)/3, x>=0$?
1. $-y=+-sqrt(5x^2)+3/4$
2. $-y=(-5x^2-4)/-3$
3. $x=(5y^2+4)/3$
4. $y=sqrt((3x-4)/5)$
8.
What is the inverse of the function $f(x) = 8x^3 - 7$?
1. $f^(-1)(x) = root3(x + 7)/(2)$
2. $f^(-1) (x) = root3(x + 7)/(8)$
3. $f^(-1)(x) = (root3 (x + 7)/2)$
4. $f^(-1)(x) = -8x^3 + 7$
9.
Which of the following is the inverse of $y=sqrt(2x^3)-8$?
1. $y=root3(-2x^2)+8$
2. $y=root3((x+8)^2/2)$
3. $x=pmsqrt(2y^3)-8$
4. $y^2=2x^3+64$
10.
Which of the following is the inverse of $y=sqrt(2x^2-8), \ x in [2,oo)$?
1. $y=+-sqrt(-2x^2+8)$
2. $y=sqrt((x^2+8)/2)$
3. $x=+-sqrt(2y^2)-8$
4. $y=2(x^2+8)^2$
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