Question

Pre calc, question 3, include both answers in bold and at the top or bottom of screen, Thanks!

Answer 1

Given the functions:

`\begin{gathered} f(x)=4x+5 \\ g(x)=2x-3 \end{gathered}`

We will find the composite function (f o g)(x)

So, we will substitute the function (f) into the function (f) as follows:

`(f\circ g)(x)=4\cdot(2x-3)+5`

Simplifying the function:

`\begin{gathered} (f\circ g)(x)=8x-12+5 \\ \\ (f\circ g)(x)=8x-7 \end{gathered}`

The resulted function is a linear function, the domain is all real numbers

`\text{Domain}=(-\infty,\infty)`

So, the answer will be:

(f o g)(x) = 8x - 7

Domain: (-∞, ∞)