Question

The figure below shows the graph of a function f(x). How many solutions does the equation $f(f(x)) = 15$ have?

From the graph of $f(x)$ :

$f(x) = 15$ occurs at $x = 4$ and $x = 12$ .
Line $y = 4$ intersects $f(x)$ at 4 points.
Line $y = 12$ intersects $f(x)$ at 3 points.

Accepted Answer

C. To solve $f(f(x)) = 15$, let $f(x) = y$. From the graph, $f(y) = 15$ for $y = 4$ and $y = 12$. Case 1: $f(x) = 4$. Horizontal line $y = 4$ intersects the graph at 4 distinct points. Case 2: $f(x) = 12$. Horizontal line $y = 12$ intersects the graph at 3 distinct points. Total solutions = $4 + 3 = 7$.

Composite Function Graph Solutions

Explanation

Practise this under exam conditions