Exponential and Logarithmic Functions: Part One — Test

Question 22 • Advanced Algebra: Concepts and Connections

Which function has an inverse that is also a function?

Answer

start set open paren negative 1 comma 2 close paren comma open paren 0 comma 4 close paren comma open paren 1 comma 5 close paren comma open paren 5 comma 4 close paren comma open paren 7 comma 2 close paren end set

start set open paren negative 1 comma 4 close paren comma open paren 0 comma 4 close paren comma open paren 1 comma 2 close paren comma open paren 5 comma 3 close paren comma open paren 7 comma 1 close paren end set

start set open paren negative 1 comma 3 close paren comma open paren 0 comma 4 close paren comma open paren 1 comma 14 close paren comma open paren 5 comma 6 close paren comma open paren 7 comma 2 close paren end set

start set open paren negative 1 comma negative 2 close paren comma open paren 0 comma 4 close paren comma open paren 1 comma 3 close paren comma open paren 5 comma 14 close paren comma open paren 7 comma 4 close paren end set

Explanation

The inverse of a function is also a function when the original function assigns different outputs to different inputs. In choice C, the outputs are 3, 4, 14, 6, and 2, so none repeat; swapping each input-output pair therefore gives an inverse that is a function. The other choices each repeat an output, which would give the inverse one input with multiple outputs.

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