Question

Given f(x)=4x2−5 and g(x)=x+3 .

What is (fg)(x) ?

Answer 1

I just took the test, it was A. 4x^3+12x^2-5x-15 :)

Answer 2

`(fg)(x)=4x^3+12x^2-5x-15`

First option is correct.

Explanation:

We have been given that

`f(x)=4x^2-5`

`g(x)=x+3`

We know that
`(fg)(x)=f(x)g(x)`

Hence, we have to find the product of f(x) and g(x)

`(fg)(x)=(4x^2-5)(x+3)`

Apply distributive property

`(fg)(x)=4x^2\cdot x+4x^2\cdot3-5x-5\cdot3`

Simplifying, we get

`(fg)(x)=4x^3+12x^2-5x-15`

First option is correct.