Chapter 9.9, Problem 32PPS

To determine

Solve the function.

Answer to Problem 32PPS

  $3x^2-x-19$

Explanation of Solution

Given Information: $f\left(x\right)=x^2-2x+14$ and $\left(f+g\right)\left(x\right)=4x^2-3x-5$

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

Calculation:

  $f\left(x\right)=x^2-2x+14$ and $\left(f+g\right)\left(x\right)=4x^2-3x-5$

Now, Use formula

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

Now, put the value of $f(x)$ and $\left(f+g\right)\left(x\right)$

  $4x^2-3x-5=x^2-2x+14+g\left(x\right)$

So,

  $g\left(x\right)=4x^2-3x-5-\left(x^2-2x+14\right)$

Hence,

  $g\left(x\right)=3x^2-x-19$