Question

f(x) = {(1, 4), (2, 3), (5, 8), (4, 7)} Is f-1(x) a function and why?

A - Yes, each element in the range has only one domain value.

B - Yes, each element in the domain has only one range value.

C - There are only a limited number of ordered pairs and can’t be determined.

D - We don’t know the original function and therefore can’t make the determination.

I know as a fact that the answer is yes, I'm confused on how to interpret it. My guesses are that it's A.

Answer 1

You are correct.

You are given f(x) explicitly, meaning all points are listed.

You can see what the domain and range of f(x) are.

For the inverse function, f^-1(x), switch the domain and range of the original function, f(x). Now each y-coordinate is part of the domain of the inverse function. Since each y-coordinate of f(x), which becomes an x-coordinate of f^-1(x), appears only once, the inverse of function f is a function.

Answer: choice A