Chapter 12.4, Problem 49STP

To determine

To find: The value of $f\left(g\left(4\right)\right)$ .

Answer to Problem 49STP

  $f\left(g\left(4\right)\right)=2$

Explanation of Solution

Given information:

The graphs of $f\left(x\right)$ and $g\left(x\right)$ .

On observing the given graph

We can say that

At $x=4$

The graph $g\left(x\right)$ cuts the X-axis.

It means

  $g\left(4\right)=0$ .

We need to find

  $f\left(g\left(4\right)\right)$

Using $g\left(4\right)=0$

We get

  $\Rightarrow f\left(g\left(4\right)\right)=f\left(0\right)$

Therefore,

At $x=0$ the graph $f\left(x\right)$ cuts the Y-axis at 2.

It means that

  $f\left(0\right)=2$

Therefore,

We get

  $\Rightarrow f\left(g\left(4\right)\right)=2$