Which of the following pairs of functions are inverses of each other?

Question

A.

and

B.

and

C.

and

D.

and

 

Answer 1

Two functions f and g are inverse functions if and only if both of their

compositions are the identity function.

That means [f o g](x) = x and [g o f](x) = x.

a)

Check to see if the compositions of f(x) and g(x) are identity functions.

Therefore, [f o g](x) and [g o f](x) are not equal, so, the functions are not inverses.

b)

Check to see if the compositions of f(x) and g(x) are identity functions.

Therefore, [f o g](x) and [g o f](x) are not equal, so, the functions are not inverses.

Answer 2

Contd....

c)

Check to see if the compositions of f(x) and g(x) are identity functions.

Therefore, [f o g](x) and [g o f](x) are not equal, so, the functions are not inverses.

d)

Check to see if the compositions of f(x) and g(x) are identity functions.

Therefore, [f o g](x) and [g o f](x) equal to x, so, the functions are inverses.