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Nonlinear Functions

SAT Math· difficulty 5/5

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

  • A

    x−1x+1\frac{x - 1}{x + 1}

  • B

    xx

    check_circle
  • C

    1x\frac{1}{x}

  • D

    x+1x−1\frac{x + 1}{x - 1}

Explanation

f(f(x))=f(x)+1f(x)−1=x+1x−1+1x+1x−1−1=(x+1)+(x−1)(x+1)−(x−1)=2x2=xf(f(x)) = \frac{f(x) + 1}{f(x) - 1} = \frac{\frac{x+1}{x-1} + 1}{\frac{x+1}{x-1} - 1} = \frac{(x+1) + (x-1)}{(x+1) - (x-1)} = \frac{2x}{2} = x.

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