Question

the tables below show some inputs and outputs of functions f and h.

x -2 -1 0 1 2 3
f(x) 1 -1 -3 -1 1 3

x -2 -1 0 1 2 3
h(x) 0.25 0.5 1 2 4 8

evaluate.

(h ∘ f)(1) =

Explanation:

Step1: Recall the definition of composition

$(h\circ f)(1)=h(f(1))$. First, find $f(1)$.

Step2: Look up $f(1)$ in the table

From the table of $f(x)$, when $x = 1$, $f(1)=-1$.

Step3: Find $h(f(1))$

Since $f(1)=-1$, then $h(f(1))=h(-1)$. Look up $h(-1)$ in the table of $h(x)$.

Step4: Look up $h(-1)$ in the table

From the table of $h(x)$, when $x=-1$, $h(-1)=0.5$.

Answer:

$0.5$