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Nonlinear Functions

SAT Math· difficulty 5/5

If f(x)=ax+bf(x) = ax + b and f(f(x))=9x+4f(f(x)) = 9x + 4, find one possible value of aa.

  • A

    a=9a = 9

  • B

    a=4a = 4

  • C

    a=3a = 3

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  • D

    a=6a = 6

Explanation

f(f(x))=a(ax+b)+b=a2x+ab+bf(f(x)) = a(ax + b) + b = a^2 x + ab + b. So a2=9⇒a=3a^2 = 9 \Rightarrow a = 3 (taking positive root).

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