Chapter 9, Problem 71SGR

To determine

To compute the value of $\left(g·h\right)\left(x\right)$ for two given functions.

Answer to Problem 71SGR

  $\left(f·h\right)\left(x\right)=-4x^2+8x^3+14x^2+6$

Explanation of Solution

Given information :

The function provided is $f\left(x\right)=4x^2-8x+2$ , $g\left(x\right)=-5x^2+x+1$ and $h\left(x\right)=3-x^2$ .

Formula used :

Use the formula $\left(f·h\right)\left(x\right)=\left(f\right)\left(x\right)\times \left(h\right)\left(x\right)$ .

  $g\left(x\right)=-5x^2+x+1$

  $h\left(x\right)=3-x^2$

These are the given functions.

  $=\left(-5x^2+x+1\right)\times \left(3-x^2\right)$

Use the property $\left(g·h\right)\left(x\right)=\left(g\right)\left(x\right)\times \left(h\right)\left(x\right)$

  $=-15x^2+5x^4+3x-x^3+3-x^2$

Arranging the items and making adjustments

  $\left(g·h\right)\left(x\right)=5x^4-x^3-16x^2+3x+3$

This is the answer.