Chapter 6.1, Problem 27PPS

To determine

If $f\left(x\right)=2x$ and $g\left(x\right)=x+5$ then find the value of $\left[f\circ g\right]\left(x\right)\text{ and }\left[g\circ f\right]\left(x\right)$ if they exist.

Answer to Problem 27PPS

The value of $\left[f\circ g\right]\left(x\right)=2x+10\text{and }\left[g\circ f\right]\left(x\right)=2x+5$ .

Explanation of Solution

Given information: The given functions are,

  $f\left(x\right)=2x$

  $g\left(x\right)=x+5$

Calculation: Evaluating $\left[f\circ g\right]\left(x\right)$ ,

  $\begin{array}{c}\left[f\circ g\right]\left(x\right)=f\left[g\left(x\right)\right]\\ =f\left(x+5\right)\\ =2\left(x+5\right)\\ =2x+10\end{array}$

Similarly, evaluating $\left[g\circ f\right]\left(x\right)$ ,

  $\begin{array}{c}\left[g\circ f\right]\left(x\right)=g\left[f\left(x\right)\right]\\ =g\left(2x\right)\\ =\left(2x\right)+5\\ =2x+5\end{array}$