Question

evaluate: $g(f(2))$

Explanation:

Step1: Find \( f(2) \) from \( y = f(x) \)

Looking at the graph of \( y = f(x) \), when \( x = 2 \), we find the corresponding \( y \)-value. The vertex of the piece - wise linear function \( f(x) \) is at \( x = 4 \) with \( y=-4 \), and for \( x = 2 \), we can see that the function value \( f(2) \) is \( - 2 \) (by following the line from the left - hand side of the vertex towards \( x = 2 \)).

Step2: Find \( g(f(2))=g(-2) \) from \( y = g(x) \)

Now we need to find the value of \( g(x) \) when \( x=-2 \). Looking at the graph of \( y = g(x) \), when \( x=-2 \), we find the corresponding \( y \)-value. From the graph of the parabola - shaped function \( g(x) \), when \( x = - 2 \), \( g(-2)=-8 \).

Answer:

\( - 8 \)