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Nonlinear Functions

SAT Math· difficulty 4/5

If f(x)=2x+1x−3f(x) = \frac{2x + 1}{x - 3}, what is f−1(x)f^{-1}(x)?

  • A

    x−32x+1\frac{x - 3}{2x + 1}

  • B

    x−12x+3\frac{x - 1}{2x + 3}

  • C

    2x−1x+3\frac{2x - 1}{x + 3}

  • D

    3x+1x−2\frac{3x + 1}{x - 2}

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Explanation

Swap and solve: x=2y+1y−3⇒x(y−3)=2y+1⇒xy−2y=3x+1⇒y=3x+1x−2x = \frac{2y + 1}{y - 3} \Rightarrow x(y - 3) = 2y + 1 \Rightarrow xy - 2y = 3x + 1 \Rightarrow y = \frac{3x + 1}{x - 2}.

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