Chapter 6.1, Problem 2AGP

To determine

The value of $\left(f·g\right)\left(x\right)$ for the pair of functions $f\left(x\right)=x^2-7x+2\text{ and }g\left(x\right)=x+4$ .

Answer to Problem 2AGP

The value $\left(f·g\right)\left(x\right)$ is equal to $x^3-3x^2-26x+8$ for the pair of functions $f\left(x\right)=x^2-7x+2\text{ and }g\left(x\right)=x+4$ .

Explanation of Solution

Given information:

The given functions are,

  $\left(\begin{array}{c}f\left(x\right)=x^2-7x+2\\ g\left(x\right)=x+4\end{array}\right)\mathrm{......}\left(1\right)$

Calculation:

Evaluating $\left(f·g\right)\left(x\right)$ using (1),

  $\begin{array}{c}\left(f·g\right)\left(x\right)=f\left(x\right)\times g\left(x\right)\\ =\left(x^2-7x+2\right)\left(x+4\right)\\ =x^3-3x^2-26x+8\end{array}$