Question

find $(f \circ g)(x)$ and $(g \circ f)(x)$.
$f(x) = |x|$, $g(x) = 15x - 8$

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

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

Explanation:

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

To find the composition \((f \circ g)(x)\), we substitute \(g(x)\) into \(f(x)\). Given \(f(x) = |x|\) and \(g(x)=15x - 8\), we replace \(x\) in \(f(x)\) with \(g(x)\). So \((f \circ g)(x)=f(g(x)) = |g(x)|=|15x - 8|\).

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

To find the composition \((g \circ f)(x)\), we substitute \(f(x)\) into \(g(x)\). Given \(g(x)=15x - 8\) and \(f(x) = |x|\), we replace \(x\) in \(g(x)\) with \(f(x)\). So \((g \circ f)(x)=g(f(x))=15f(x)-8 = 15|x|-8\).

Answer:

\((f \circ g)(x)=\boldsymbol{|15x - 8|}\)
\((g \circ f)(x)=\boldsymbol{15|x| - 8}\)