Question

Consider the graph of a real-valued continuous function $f\left(x\right)$ defined on $R$ (the set of real numbers) as shown below.


The number of real solutions of the equation $f\left(f\right(x\left)\right)=4$ is

Answer 1

Put $f\left(x\right)=t$
Then, $f\left(t\right)=4$
$\Rightarrow t=-2,0,4$
Now, $f\left(x\right)=-2$ for two values of $x$.
$f\left(x\right)=0$ for two values of $x$.
and $f\left(x\right)=4$ for three values of $x$.
Hence, the number of real solutions of the equation $f\left(f\right(x\left)\right)=4$ is $7$.