Chapter 9.9, Problem 15PPS

To determine

Solve the function.

Answer to Problem 15PPS

  $2^x-7+x^2$

Explanation of Solution

Given Information: $f\left(x\right)=-x^2+9$ , $g\left(x\right)=2^x+2$ and $h\left(x\right)=3x^2-6x-9$

Formula Used: $\left(g-f\right)\left(x\right)=g(x)-f\left(x\right)$

Calculation:

  $f\left(x\right)=-x^2+9$ , $g\left(x\right)=2^x+2$ and $h\left(x\right)=3x^2-6x-9$

Now, Use formula

  $\left(g-f\right)\left(x\right)=g(x)-f\left(x\right)$

Now, put the value of $g(x)$ and $f(x)$

  $\left(g-f\right)\left(x\right)=2^x+2-\left(-x^2+9\right)$

Hence,

  $\left(g-f\right)\left(x\right)=2^x-7+x^2$