Suppose that f: X→Y and g: Y→Z are functions. Please teach me how to write the convers and inverse of the following statement. And what is a counter example of the converse? If both f and g are one-to-one, then g(f(x)): X→Z is one to one.

9. Consider the function y = (x + 1)². (a.) y = (x + 1)2 is not a one-to-one function. Restrict its domain to create a one-to-one function f. What is the domain and range of f? (b.) Find the inverse of f. What is the domain and range of f-1?

Please answer this WITHOUT A CALCULATOR. Your answer must match ONE of the answer choices. there is only ONE solution. If your answer is none of these choices than your answer is wrong and please check your math.

The given function f(x) = x3 + 2 is all one-to-one. For this function, a. Find an equation for f -1(x), the inverse function. b. Verify that your equation is correct by showing that f( f -1(x)) = x and f -1( f(x)) = x.