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Linear Functions

SAT Math· difficulty 5/5

Function f(x)=(k−1)x+3f(x) = (k - 1)x + 3 has the property f−1(x)=f(x)f^{-1}(x) = f(x) for all xx. What is kk?

  • A

    −1-1

  • B

    11

  • C

    00

    check_circle
  • D

    22

Explanation

A linear function equals its own inverse iff slope =−1= -1 and the line passes through fixed point with that intercept relation. (k−1)=−1⇒k=0(k - 1) = -1 \Rightarrow k = 0.

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