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