evaluate each expression using the graphs of y = f(x) and y = g(x) shown.\n(a) (g ∘ f)( - 1) (b) (g ∘ f)(0)…

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

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

Answer

Explanation:

Step1: Recall composition of functions

$(g\circ f)(x)=g(f(x))$. First find $f(-1)$. Looking at the graph of $y = f(x)$, when $x=-1$, $f(-1)= - 2$.

Step2: Evaluate $g(f(-1))$

Since $f(-1)=-2$, then $(g\circ f)(-1)=g(f(-1)) = g(-2)$. Looking at the graph of $y = g(x)$, when $x = - 2$, $g(-2)=6$.

Answer:

$6$