1 Answer

Fhofmann · Answer 1 · 2023-01-05T08:27:12+0000

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: (-∞, ∞)

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