Chapter 9, Problem 70SGR

To determine

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

Answer to Problem 70SGR

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

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

  $f\left(x\right)=4x^2-8x+2$

  $h\left(x\right)=3-x^2$

These are the given functions.

  $=\left(4x^2-8x+2\right)\times \left(3-x^2\right)$

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

  $=4x^2\times 3-4x^2\times x^2-8x\times 3+8x\times x^2+2\times 3+2\times x^2$

Arranging the items.

  $=12x^2-4x^4-24x+8x^3+6+2x^2$

Making adjustments

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

This is the answer.