Question

The range of a function is the domain of its inverse.

A. True
B. False

Answer 1

So to find the domain and range of the inverse, you swap the domain and range from the original function.

Therefore, I would say this is A, true.

Answer 2

Yes but this is not a way to define range as most functions do not have an inverse.

Answer 3

Often we have to restrict the domain of the function to be able to obtain its inverse. such example would be \(f(x)=\sin(x)\)

Answer 4

Which is actually a poor name, and should be called it's restricted inverse. But they can only throw so many things at them...

Answer 5

But then again, asking you the domain of a function does not make any sense at all. A function is defined by it's domain. So you don't know the function unless you know the domain. To be correct, they would have to ask for the maximal subset of the reals that would allow this rule to produce a well defined/ defined everywhere relation.