Question

If f(x) = 2x + 3 and g(x) = 3x - 9, find f(g(x)).6x6x - 156x - 186x - 6None of the choices are correct.

Answer 1

The expression f(g(x)) refers to the function composition. That term is defined as follows:

$f\circ g(x)=f(g(x))$

Let's suppose that x is in the domain of g, then

$g(x)=y$

And we need to find f(y):

$\begin{gathered} g(x)=3x-9 \\ \Rightarrow f(g(x))=f(y)=2y+3=2(3x-9)+3 \\ \Rightarrow f(g(x))=6x-18+3=6x-15 \\ \Rightarrow f(g(x))=6x-15 \end{gathered}$

Therefore, the answer to the question is the second option 6x-15