Question

Find the indicated values, where

Answer 1

A.

Firstly, you should deal with the inner function.

1^2 - 1 = 0

And

2 x 0 = 0

So 2g(1) = 0

Applying the outer function:

0 + 1 = 1

Answer 2

For this case we have, that given two functions f (x) and g (x), then:

The composite function of f with g is:
`(gof) (x) = g [f (x)]`

The function composed of g with f is:
`(fog) (x) = f [g (x)]`

In this case we have:

`f (x) = 1 + x\\g (t) = t ^ 2-1`

First we solve g (1):

`g (1) = 1 ^ 2-1 = 0`

Now:

`2 * g (1) = 2 * 0 = 0`

Then we have left:

`f (0) = 1 + 0 = 1`

So, we have to:

`f (2g (1)) = 1`

Answer:

Option A