Question

3 numeric 1 point if $f(x) = j circ h$ then $f(1) =?$ answer 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 $f(3) =?$ for all questions use the following functions: $g(x) = 3x + 2$ $h(x) = \frac{2}{x}$ $j(x) = x^2 - 1$

Explanation:

Question 3

Step1: Recall function composition

Function composition \( f(x) = j \circ h \) means \( f(x) = j(h(x)) \). First, find \( h(1) \).
\( h(x) = \frac{2}{x} \), so \( h(1) = \frac{2}{1} = 2 \).

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

\( j(x) = x^2 - 1 \), so \( j(h(1)) = j(2) = 2^2 - 1 = 4 - 1 = 3 \).

Step1: Recall function composition

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

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

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

Step1: Recall function composition

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

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

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

Answer:

3

Question 4