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Linear Functions

SAT Math· difficulty 4/5

Suppose f(x)=ax+1f(x) = ax + 1 and f(f(1))=13f(f(1)) = 13. If a>0a > 0, what is aa?

  • A

    44

  • B

    33

    check_circle
  • C

    55

  • D

    22

Explanation

f(1)=a+1f(1) = a + 1. f(f(1))=a(a+1)+1=a2+a+1=13f(f(1)) = a(a+1) + 1 = a^2 + a + 1 = 13, so a2+a−12=0a^2 + a - 12 = 0, giving a=3a = 3 (positive root).

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