Q 10. - Precalculus Enhanced with Graphing Utilities

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

Step-by-Step Solution

Answer

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

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 

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