Question

# Consider the graph of a real-valued continuous function f(x) defined on R (the set of real numbers) as shown below. The number of real solutions of the equation f(f(x))=4 is

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Solution

## Put f(x)=t Then, f(t)=4 ⇒t=−2,0,4 Now, f(x)=−2 for two values of x. f(x)=0 for two values of x. and f(x)=4 for three values of x. Hence, the number of real solutions of the equation f(f(x))=4 is 7.

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