Question

let $f(x) = \frac{1}{x - 2}$ and $g(x) = 2x + 5$. then $(f \circ g)(2) = \square$, $(f \circ g)(x) = \square$. question help: \boxed{message instructor} \boxed{calculator}

Explanation:

Step1: Compute $g(2)$

$g(2)=2(2)+5=4+5=9$

Step2: Compute $f(g(2))=f(9)$

$f(9)=\frac{1}{9-2}=\frac{1}{7}$

Step3: Find $(f\circ g)(x)=f(g(x))$

Substitute $g(x)=2x+5$ into $f$:
$f(g(x))=\frac{1}{(2x+5)-2}=\frac{1}{2x+3}$

Answer:

$(f \circ g)(2) = \frac{1}{7}$
$(f \circ g)(x) = \frac{1}{2x+3}$