Question

practice assignment 3.4 composition of functions
score: 60/80 answered: 6/8
question 7
the function $h(x)=\frac{1}{x - 6}$ can be expressed in the form $f(g(x))$, where $g(x)=(x - 6)$, and $f(x)$ is defined as:
$f(x) = $

Explanation:

Step1: Identify composite function structure

We know $h(x) = f(g(x))$, with $g(x)=x-6$ and $h(x)=\frac{1}{x-6}$.

Step2: Substitute $g(x)$ into composite form

Replace $g(x)$ in $f(g(x))$ with $x-6$, so $f(x-6)=\frac{1}{x-6}$.

Step3: Find $f(x)$ by substitution

Let $t = g(x) = x-6$. Then $f(t)=\frac{1}{t}$. Renaming $t$ to $x$, we get $f(x)=\frac{1}{x}$.

Answer:

$\boldsymbol{f(x) = \frac{1}{x}}$