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Nonlinear Functions

SAT Math· difficulty 4/5

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

  • A

    x+2x + 2

  • B

    1x+2\frac{1}{x + 2}

  • C

    1x\frac{1}{x}

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  • D

    1x−4\frac{1}{x - 4}

Explanation

f(g(x))=1g(x)−2=1(x+2)−2=1xf(g(x)) = \frac{1}{g(x) - 2} = \frac{1}{(x + 2) - 2} = \frac{1}{x}.

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