Question

evaluate each expression using the graphs of ( y = f(x) ) and ( y = g(x) ) shown below. (a) ( (g circ f)(-1) ) (b) ( (g circ f)(0) ) (c) ( (f circ g)(-1) ) (d) ( (f circ g)(4) ) (a) ( (g circ f)(-1)=4 ) (simplify your answer.) (b) ( (g circ f)(0)=square ) (simplify your answer.)

Explanation:

Step1: Find \( f(0) \)

From the graph of \( y = f(x) \), when \( x = 0 \), \( f(0)=-1 \)

Step2: Calculate \( (g\circ f)(0)=g(f(0)) \)

Since \( f(0)=-1 \), then \( (g\circ f)(0)=g(-1) \)
From the graph of \( y = g(x) \), when \( x=-1 \), \( g(-1) = 6 \)

Answer:

\( 6 \)