Chapter 6.4, Problem 59E

To determine

To calculate: The value of $\left(f+g\right)\left(x\right)$ and then its value when $x=2$ .

Answer to Problem 59E

The value of $\left(f+g\right)\left(x\right)$ is $14x^3$ and the value of the difference when $x=2$ is $\left(112\right)$ .

Explanation of Solution

Given information: The given functions are $f\left(x\right)=6x^3$ and $g\left(x\right)=8x^3$ .

Calculation:

It is clear that

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

Put the values of $f\left(x\right)$ and $g\left(x\right)$ into the equation.

  $\left(f+g\right)\left(x\right)=6x^3+8x^3$

  $\left(f+g\right)\left(x\right)=14x^3$

Hence, the value of $\left(f+g\right)\left(x\right)$ is $14x^3$ .

Now, find the value of $\left(f+g\right)\left(x\right)$ when $x=2$ .

  $\left(f+g\right)\left(x\right)=14x^3$

Substitute $x=2$ in the obtained value of $\left(f+g\right)\left(x\right)$ .

  $\left(f+g\right)\left(x\right)=14{\left(2\right)}^3$

  $\left(f+g\right)\left(x\right)=14\left(8\right)$

  $\left(f+g\right)\left(x\right)=112$

Hence, the value of the difference when $x=2$ is $\left(112\right)$ .