Question

Please help with this math question!

Answer 1

Explanation:

The little circle between the f and g is another way of saying multiplication. So we'll multiply f(x) and g(x)

`(4 {x}^(2) + 5x)(3x + 4)`

What we do next is distribute.

`12 {x}^(3) + 16 {x}^(2) + 15 {x}^(2) + 20x`

Now, we combine like terms

`12 {x}^(3) + 31 {x}^(2) + 20x`

Answer 2

12
`x^(2)` + 15x + 4

Explanation:

(f ° g)(x) means a composition of functions. It can also be written as f(g(x)).

This means that you are taking g(x) and plugging it into f(x) anywhere there is an x in the equation.

f(x) = 3x + 4

f(g(x)) = 3(g(x)) + 4

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

= 12
`x^(2)` + 15x + 4