Choose any two specific functions (not already chosen by a classmate) that have inverses. Use your chosen functions to answer any one of the following questions:

If the inverses of two functions are both functions, will the inverse of the sum or difference of the original functions also be a function?

Answer: let's took f and g, injectives, with inverses F and G.

the condition for a function to have an inverse, is that the function must be injective, it means that if f (x1) = f (x2), then x1 = x2

So f and g are injective, then f + g is injective.

we need to see that if (f + g) (x1) = (f + g) (x2) then x1 = x2

Now think on a counterexample for this.

if f (x) = 2x, and g (x) = - 2x (both of them are injective)

then f (x) + g (x) = 0, so its not injective, so the inverse is not a function.

but f (x) - g (x) = 4x, which is injective and his inverse is a function.

Then the statement is false, because the fact that the inverses of f and g are functions, doesn't imply that the inverse of their sum or difference is also a function.

Did u ever find the answer?