Function Inverses — Quiz

Question 2 • Mathematics III

Which function has an inverse that is also a function?

Answer

start set open paren negative 4 comma 3 close paren comma open paren negative 2 comma 7 close paren comma open paren negative 1 comma 0 close paren comma open paren 4 comma negative 3 close paren comma open paren 11 comma negative 7 close paren end set

start set open paren negative 4 comma 6 close paren comma open paren negative 2 comma 2 close paren comma open paren negative 1 comma 6 close paren comma open paren 4 comma 2 close paren comma open paren 11 comma 2 close paren end set

start set open paren negative 4 comma 5 close paren comma open paren negative 2 comma 9 close paren comma open paren negative 1 comma 8 close paren comma open paren 4 comma 8 close paren comma open paren 11 comma 4 close paren end set

start set open paren negative 4 comma 4 close paren comma open paren negative 2 comma negative 1 close paren comma open paren negative 1 comma 0 close paren comma open paren 4 comma 1 close paren comma open paren 11 comma 1 close paren end set

Explanation

A function has an inverse that is also a function when each output value is paired with only one input. In choice A, the outputs are 3, 7, 0, −3, and −7, and none repeat. The other choices each repeat an output, so their inverses would assign one input to more than one output.

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