Chapter 1, Problem 18SGA

To determine

To find: $\left(f+g\right)\left(x\right),\left(f-g\right)\left(x\right),\left(f\cdot g\right)\left(x\right)\text{ and }\left(\frac{f}{g}\right)\left(x\right)$

Answer to Problem 18SGA

  $\begin{array}{c}\left(f+g\right)\left(x\right)=6x-2\\ \left(f-g\right)\left(x\right)=6x-6\\ \left(f\cdot g\right)\left(x\right)=12x-8\\ \left(\frac{f}{g}\right)\left(x\right)=3x-2\end{array}$

Explanation of Solution

Given information: The functions given are as follows:

  $\begin{array}{l}f\left(x\right)=6x-4\\ g\left(x\right)=2\end{array}$

Calculation:

Put the values of $f\left(x\right)$ and $g\left(x\right)$ in the equation below and simplify as follows:

  $\begin{array}{c}\left(f+g\right)\left(x\right)=f\left(x\right)+g\left(x\right)\\ =6x-4+2\\ =6x-2\end{array}$

Thus, the value of $\left(f+g\right)\left(x\right)$ is $6x-4$ .

Put the values of $f\left(x\right)$ and $g\left(x\right)$ in the equation below and simplify as follows:

  $\begin{array}{c}\left(f-g\right)\left(x\right)=f\left(x\right)-g\left(x\right)\\ =6x-4-2\\ =6x-6\end{array}$

Thus, the value of $\left(f-g\right)\left(x\right)$ is $6x-6$ .

Put the values of $f\left(x\right)$ and $g\left(x\right)$ in the equation below and simplify as follows:

  $\begin{array}{c}\left(f\cdot g\right)\left(x\right)=f\left(x\right)\cdot g\left(x\right)\\ =\left(6x-4\right)\left(2\right)\\ =12x-8\end{array}$

Thus, the value of $\left(f\cdot g\right)\left(x\right)$ is $12x-8$ .

Put the values of $f\left(x\right)$ and $g\left(x\right)$ in the equation below and simplify as follows:

  $\begin{array}{c}\left(\frac{f}{g}\right)\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}\\ =\frac{6x-4}{2}\\ =3x-2\end{array}$

Thus, the value of $\left(\frac{f}{g}\right)\left(x\right)$ is $3x-2$ .