Question

Please Help!!!!!!!

Given that f(x) = 4x +1 and g(x) = x^2 -2,

which of the following is an expression for f(g(x))?

a. 16x^2 + 8x - 1
b. x^2 + 4x - 1
c. 5x^2 - 1
d. 4x^2 - 7

Answer 1

d.
`4x^2-7`

Explanation:

The given functions are

`f(x)=4x+1` and
`g(x)=x^2-2`

We want to find the composition of the f and g.

`f(g(x))=f(x^2-2)`

We substitute
`x^2-2` into
`f(x)=4x+1` to obtain;

`f(g(x))=4(x^2-2)+1`

This simplifies to;

`f(g(x))=4x^2-8+1`

`f(g(x))=4x^2-7`

Hence the correct choice is d.