Which of the following is true of functions and their inverses a) the inverse of a linear function is always a function. b) the inverse of a quadratic function is always a function. c) the inverse of a linear function is not a function. d) the inverse of a quadratic function is not a function.

We know the following facts:
1. Linear relationships are functions EXCEPT for vertical lines.
2. The inverse of a linear function is also linear (therefore are functions) EXCEPT for constant functions, whose inverse is a vertical line.
3. All polynomials (including quadratic functions) are functions.
4. The inverse of even-degree polynomials are never functions (because the end-behaviours are either both positive or both negative).

From this we can conclude that
a) the inverse of a linear function is always a function.
    FALSE:  a (linear) constant function has a vertical line as the inverse, so  not always true.
b) the inverse of a quadratic function is always a function.
    FALSE: inverse of of a quadratic function is NEVER a function
c) the inverse of a linear function is not a function.
    FALSE: not always true, so false.
d) the inverse of a quadratic function is not a function.
    TRUE: as explained in note (4) above.

What’s your question.