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Nonlinear Functions

SAT Math· difficulty 4/5

What is the inverse of f(x)=ex−1f(x) = e^x - 1?

  • A

    f−1(x)=ln⁡(x)−1f^{-1}(x) = \ln(x) - 1

  • B

    f−1(x)=ex+1f^{-1}(x) = e^{x + 1}

  • C

    f−1(x)=ln⁡(x+1)f^{-1}(x) = \ln(x + 1)

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  • D

    f−1(x)=ln⁡(x−1)f^{-1}(x) = \ln(x - 1)

Explanation

y=ex−1⇒y+1=ex⇒x=ln⁡(y+1)y = e^x - 1 \Rightarrow y + 1 = e^x \Rightarrow x = \ln(y + 1), so f−1(x)=ln⁡(x+1)f^{-1}(x) = \ln(x + 1).

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