Chapter 9.9, Problem 50HP

To determine

Solve the function.

Answer to Problem 50HP

Quadratic function.

Explanation of Solution

Given Information: $f\left(x\right)$ is linear function and $g\left(x\right)$ is quadratic function.

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

Calculation:

  $f\left(x\right)$ is linear function and $g\left(x\right)$ is quadratic function.

  $f\left(x\right)=4x+1$ and $g\left(x\right)=x^2-5x-9$

Now, to find $\left(f+g\right)\left(x\right)$ , Use formula

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

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

  $\left(f+g\right)\left(x\right)=4x+1+x^2-5x-9$

Hence,

  $\left(f+g\right)\left(x\right)=x^2-x-8$

If $f\left(x\right)$ is linear function and $g\left(x\right)$ is quadratic function then $\left(f+g\right)\left(x\right)$ is the sum of linear and quadratic function.

So, it is a quadratic function.