Question

find $(f\circ g)\left(x\right)$and $(g\circ f)\left(x\right)$and graph each of these functions.
role="math" localid="1646574166664" $$\begin{gathered} f\left(x\right)=-2x \\ g\left(x\right)=\cos x \end{gathered}$$

Short answer

If$f\left(x\right)=-2x\&g\left(x\right)=\cos x$then $(g\circ f)\left(x\right)=\cos (-2x)and(f\circ g)\left(x\right)=-2\cos x$and their graph is

Step-by-step solution

Step 1. Given data 

The given functions are

$$\begin{gathered} f\left(x\right)=-2x \\ g\left(x\right)=\cos x \end{gathered}$$

Step 2. compositions of functions 

Composition $(f\circ g)\left(x\right)$is

$$\begin{gathered} (f\circ g)\left(x\right)=f\left(g\right(x\left)\right) \\ =f\left(\cos \right(x\left)\right) \\ =-2\cos x \end{gathered}$$

Step 3. compositions of functions 

Composition$(g\circ f)\left(x\right)$is

$$\begin{gathered} (g\circ f)\left(x\right)=g\left(f\right(x\left)\right) \\ =g(-2x) \\ =\cos (-2x) \end{gathered}$$

Step 4. Graph of the composition of functions 

Plot the graph of $(f\circ g)\left(x\right)=-2\cos x$and$(g\circ f)\left(x\right)=\cos (-2x)$