Given the functions:
[tex]\begin{gathered} f(x)=4x+5 \\ g(x)=2x-3 \end{gathered}[/tex]
We will find the composite function (f o g)(x)
So, we will substitute the function (f) into the function (f) as follows:
[tex](f\circ g)(x)=4\cdot(2x-3)+5[/tex]
Simplifying the function:
[tex]\begin{gathered} (f\circ g)(x)=8x-12+5 \\ \\ (f\circ g)(x)=8x-7 \end{gathered}[/tex]
The resulted function is a linear function, the domain is all real numbers
[tex]\text{Domain}=(-\infty,\infty)[/tex]
So, the answer will be:
(f o g)(x) = 8x - 7
Domain: (-∞, ∞)
