The function f(x) = ax + b satisfies f(f(x)) = 4x + 9 for all x, and a 0. What is a + b?

5 f(f(x)) = a(ax + b) + b = a^2 x + ab + b = 4x + 9. So a^2 = 4 \Rightarrow a = 2 (positive). Then b(a + 1) = 9 \Rightarrow 3b = 9 \Rightarrow b = 3. a + b = 5.

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Acemy

Linear Functions

SAT Math· difficulty 5/5

f(x) = ax + b

A
$5$
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B
$7$
C
$3$
D
$11$

Explanation

f(f(x)) = a(ax + b) + b = a^2 x + ab + b = 4x + 9

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