Question

given the functions:
$f(x)=7x$
$g(x)=|x - 2|$
$h(x)=\frac{1}{x - 4}$
evaluate the function $(hcirc g)(5)$ for the given value of $x$. write your answer as an integer or simplified fraction. select \undefined\ if applicable.
$(hcirc g)(5)$ is .

Explanation:

Step1: Understand the function composition

The notation \((h \cdot g)(x)\) means \(h(g(x))\), so we first need to find \(g(5)\) and then substitute that result into \(h(x)\).

Step2: Calculate \(g(5)\)

Given \(g(x) = |x - 2|\), substitute \(x = 5\):
\(g(5)=|5 - 2|=|3| = 3\)

Step3: Calculate \(h(g(5)) = h(3)\)

Given \(h(x)=\frac{1}{x - 4}\), substitute \(x = 3\):
\(h(3)=\frac{1}{3 - 4}=\frac{1}{-1}=-1\)

Answer:

\(-1\)