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Nonlinear Functions

SAT Math· difficulty 3/5

What is the inverse of f(x)=3x−6f(x) = 3x - 6?

  • A

    f−1(x)=3x+6f^{-1}(x) = 3x + 6

  • B

    f−1(x)=x+63f^{-1}(x) = \frac{x + 6}{3}

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  • C

    f−1(x)=x−63f^{-1}(x) = \frac{x - 6}{3}

  • D

    f−1(x)=13x−6f^{-1}(x) = \frac{1}{3x - 6}

Explanation

Let y=3x−6y = 3x - 6. Swap and solve: x=3y−6⇒y=x+63x = 3y - 6 \Rightarrow y = \frac{x + 6}{3}.

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