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Linear Functions

SAT Math· difficulty 4/5

For linear functions ff and gg, suppose f(g(x))=6x−7f(g(x)) = 6x - 7 and g(x)=2x+1g(x) = 2x + 1. What is f(x)f(x)?

  • A

    3x−103x - 10

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  • B

    3x+13x + 1

  • C

    3x−43x - 4

  • D

    3x−73x - 7

Explanation

Let f(u)=au+bf(u) = au + b. f(2x+1)=a(2x+1)+b=2ax+a+b=6x−7f(2x + 1) = a(2x + 1) + b = 2ax + a + b = 6x - 7. So a=3a = 3, a+b=−7⇒b=−10a + b = -7 \Rightarrow b = -10. f(x)=3x−10f(x) = 3x - 10.

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