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Nonlinear Functions

SAT Math· difficulty 5/5

If f(x)=x−1f(x) = \sqrt{x - 1} and f(g(x))=x2−1f(g(x)) = \sqrt{x^2 - 1}, what is g(x)g(x)?

  • A

    x−1x - 1

  • B

    x\sqrt{x}

  • C

    x2−1x^2 - 1

  • D

    x2x^2

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Explanation

f(g(x))=g(x)−1=x2−1f(g(x)) = \sqrt{g(x) - 1} = \sqrt{x^2 - 1}, so g(x)−1=x2−1g(x) - 1 = x^2 - 1, giving g(x)=x2g(x) = x^2.

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