Question

find (f ∘ g)(x) and (g ∘ f)(x).
f(x) = |x|, g(x) = 15x - 2

(f ∘ g)(x) =
(g ∘ f)(x) =

Explanation:

Step1: Find \((f \circ g)(x)\)

By the definition of function composition, \((f \circ g)(x)=f(g(x))\). We substitute \(g(x) = 15x - 2\) into \(f(x)\). Since \(f(x)=\vert x\vert\), we replace \(x\) with \(15x - 2\) in \(f(x)\). So \(f(g(x))=\vert 15x - 2\vert\).

Step2: Find \((g \circ f)(x)\)

By the definition of function composition, \((g \circ f)(x)=g(f(x))\). We substitute \(f(x)=\vert x\vert\) into \(g(x)\). Since \(g(x)=15x - 2\), we replace \(x\) with \(\vert x\vert\) in \(g(x)\). So \(g(f(x)) = 15\vert x\vert- 2\).

Answer:

\((f \circ g)(x)=\vert 15x - 2\vert\)
\((g \circ f)(x)=15\vert x\vert - 2\)