Question

Which two functions are inverses of each other? A. f(x) = x, g(x) = –x B. f(x) = 2x, g(x) = -1/2x C. f(x) = 4x, g(x) = 1/4x D. f(x) = –8x, g(x) = 8x

Answer 1

Answer:

The correct option is C) $f(x)=4x \ \text{and} \ g(x)=\frac{x}{4}$

Step-by-step explanation:

We need to find out the pair of functions which are inverse of each other

A) $f(x)=x \ \text{and} \ g(x)=-x$

  Since, $(fog)(x)=f(g(x))=-x$

   and   $(gof)(x)=g(f(x))=-x$    

So, these are not inverse of each others

B) $f(x)=2x \ \text{and} \ g(x)=\frac{-x}{2}$

  Since, $(fog)(x)=f(g(x))=2(\frac{-x}{2})=-x$

   and   $(gof)(x)=g(f(x))=\frac{-2x}{2}=-x$    

So, these are not inverse of each others

C) $f(x)=4x \ \text{and} \ g(x)=\frac{x}{4}$

  Since, $(fog)(x)=f(g(x))=4(\frac{x}{4})=x$

   and   $(gof)(x)=g(f(x))=\frac{4x}{4}=x$    

So, these are inverse of each others

D) $f(x)=-8x \ \text{and} \ g(x)=8x$

  Since, $(fog)(x)=f(g(x))=-8(8x)=-64x$

   and   $(gof)(x)=g(f(x))=8(-8x)=-64x$    

So, these are not inverse of each others

Therefore the correct option is C) $f(x)=4x \ \text{and} \ g(x)=\frac{x}{4}$

Answer 2

B. f(x)=2x, g(x)= -1/2x. Hope this helps. :-)