Question

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 1

Did u ever find the answer?

Answer 2

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.