Question

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

Find the number of real solutions of the equation $f(f(x))=4$

Answer 1

Answer: 7

Put $f(x)=t\Rightarrow f(t)=4\Rightarrow t=-2,0,4$
Hence $f(x)=-2\Rightarrow 2$ values of $x$.
or$f(x)=0\Rightarrow 2$ values of $x$.
or $f(x)=4\Rightarrow 3$ values of $x$.
Hence, the number of real solutions of the equation$f(f(x))=4$are $7$.