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Inverse Functions (Grades 11-12)

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Inverse Functions

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