2002 AMC 12A Problem 19 — Solution | LIVE by Po-Shen Loh

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2002 AMC 12A Problem 19

Below is the professionally curated solution for Problem 19 of the 2002 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2002 AMC 12A solutions, or check the answer key.

All of the real AMC 8, AMC 10, AMC 12, and AIME problems in our complete solution collection are used with official legal permission of the Mathematical Association of America (MAA).

Concepts:function data and graph interpretation

Difficulty rating: 1660

19.

The graph of the function $f$ is shown below. How many solutions does the equation $f(f(x)) = 6$ have?

$2$

$4$

$5$

$6$

$7$

Solution:

The graph reaches $6$ at $x = -2$ and $x = 1,$ so $f(f(x)) = 6$ requires $f(x) = -2$ or $f(x) = 1.$

The horizontal line $y = -2$ meets the graph twice, and $y = 1$ meets it four times, giving $2 + 4 = 6$ solutions.

Thus, the correct answer is D.

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