Question

Given f(x) = 4x + 1 and g(x) = x^, choose
the expression for (fᵒg)(x).

Answer 1

`(fog)(x)=4x^2+1`

Explanation:

Assume
`g(x)=x^2`

`(fog)(x)` is a composition of two functions such that
`(fog)(x)=f(g(x))`.

Consider the function:

`f(x)=4x+1`

Replace
`x` with
`g(x)` into the equation:

`f(g(x))=4\cdot g(x)+1`

Substitute
`g(x)=x^2` on the right side of the equation:

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

Therefore, the expression for
`(fog)(x)` is
`4x^2+1`.

Answer 2

Answer: 4x^2 + 1

Explanation:

I am assuming g(x) = x^2

4(x^2) + 1

4x^2 + 1