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

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

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

Answer

Explanation:

Step1: Recall composition of functions definition

$(g\circ f)(x)=g(f(x))$. First find $f(-1)$ from the graph of $y = f(x)$.

Step2: Locate $x=-1$ on $y = f(x)$ graph

Suppose from the graph of $y = f(x)$, when $x=-1$, $f(-1)=1$.

Step3: Evaluate $g(f(-1))$

Now we need to find $g(1)$. Locate $x = 1$ on the graph of $y = g(x)$. Suppose from the graph of $y = g(x)$, when $x = 1$, $g(1)=3$. So $(g\circ f)(-1)=3$.

Answer:

$3$