Question

Evaluate each expression using the graphs of $y=f\left(x\right)$and $y=g\left(x\right)$as shown in the given figure.

(a) $\left(g\circ f\right)\left(1\right)$(b) $\left(g\circ f\right)\left(5\right)$(c) $\left(f\circ g\right)\left(0\right)$(d) $\left(f\circ g\right)\left(2\right)$.

Short answer

The value is (a) 3 (b) 4 (c) 1 (d) -2.

Step-by-step solution

Part (a) Step 1. Given information.

Evaluate each expression using the graphs of $y=f\left(x\right)$and $y=g\left(x\right)$.

Part (a) Step 2. Evaluation of a functional value.

The functional value is

$\left(g\circ f\right)\left(1\right)=g\left(f\left(1\right)\right)=g\left(-1\right)=3$.

Part (b) Step 1. Given Information.

Evaluate each expression using the graphs of $y=f\left(x\right)\&y=g\left(x\right)$.

Part (b) Step 2. Evaluation of a functional value. 

The functional value is

$\left(g\circ f\right)\left(5\right)=g\left(f\left(5\right)\right)=g\left(1\right)=4$.

Part (c) Step 1. Given Information.

Evaluate each expression using the graphs of $y=f\left(x\right)\&y=g\left(x\right)$.

Part (c) Step 2. Evaluation of a functional value. 

The functional value is

$\left(f\circ g\right)\left(0\right)=f\left(g\left(0\right)\right)=f\left(5\right)=1$.

Part (d) Step 1. Given information.

Evaluate each expression using the graphs of $y=f\left(x\right)\&y=g\left(x\right)$.

Part (d) Step 2. Evaluation of a functional value. 

The functional value is

$\left(f\circ g\right)\left(2\right)=f\left(g\left(2\right)\right)=f\left(2\right)=-2$.