Question

4 numeric 1 point
if $f(x) = h \circ g$ then $f(2) =?$
answer

5 numeric 1 point
if $f(x) = h \circ j$ then $f(3) =?$
answer

6 numeric 1 point
if $f(x) = g \circ g$ then $f(2) =?$
answer

for all questions use the following functions:

$g(x) = 3x + 2$ $h(x) = \frac{2}{x}$ $j(x) = x^2 - 1$

Explanation:

Question 4:

Step1: Recall function composition

Function composition \( f(x) = h \circ g \) means \( f(x) = h(g(x)) \). First, find \( g(2) \).
\( g(2) = 3(2) + 2 = 6 + 2 = 8 \)

Step2: Substitute into \( h(x) \)

Now, substitute \( g(2) = 8 \) into \( h(x) \). \( h(8) = \frac{2}{8} = \frac{1}{4} \)

Step1: Recall function composition

\( f(x) = h \circ j \) means \( f(x) = h(j(x)) \). First, find \( j(3) \).
\( j(3) = 3^2 - 1 = 9 - 1 = 8 \)

Step2: Substitute into \( h(x) \)

Substitute \( j(3) = 8 \) into \( h(x) \). \( h(8) = \frac{2}{8} = \frac{1}{4} \)

Step1: Recall function composition

\( f(x) = g \circ g \) means \( f(x) = g(g(x)) \). First, find \( g(2) \).
\( g(2) = 3(2) + 2 = 8 \)

Step2: Substitute into \( g(x) \) again

Now, substitute \( g(2) = 8 \) into \( g(x) \). \( g(8) = 3(8) + 2 = 24 + 2 = 26 \)

Answer:

\(\frac{1}{4}\)

Question 5: