Question

Consider the two functions shown below.

Answer 1

Correct choice is A.

Explanation:

Given functions are
`f\left(x\right)=5x-11` and
`g\left(x\right)=(1)/(5)x+11`.

Then
`f\left(g\left(x\right)\right)=f\left((1)/(5)x+11\right)=5\left((1)/(5)x+11\right)-11=x+55-11=x+44`

By definition of inverse we says that if f(x) and g(x) are inverse of each other then f(g(x)) must be equal to x.

But in above calculation we can see that f(g(x)) is not equal to x.

Hence correct choice is A.

Answer 2

The correct answer is A

EXPLANATION

If the two functions are inverses , then

`f(g(x)) = g(f(x)) = x`

Given

`f(x) = 5x - 11`

and

`g(x) = (1)/(5)x + 11`

`f(g(x)) = f( (1)/(5) x + 11)`

This implies that,

`f(g(x)) = 5((1)/(5) x + 11) - 11`

Expand to get;

`f(g(x)) =x + 55 - 11`

`f(g(x)) =x +44`

Since

`f(g(x)) \\e \: x`

The two functions are not inverses

The correct answer is A