Alg 2 question. Need help thank you!

Question

A. For what domain are f(x) = x² and  inverse functions? Make sure you use set builder notation.

B. Explain how you can tell that f(x) = x³ and  are inverse functions. Explain.

C. List two more functions that are inverses of each other.

D. List a function besides f(x) = -x, f(x) = x, f(x) = 1/x, or f(x) = -1/x that is its own inverse.

Answer 1

A. If it doesn't involve complex numbers, then ∀ x ∈ R ∣ x≥0

B. By definition:  g(f(x))=x . Remember that function f: X → Y should satisfy that for every y in Y, there is exactly one x in X such that f(x) = y IN ORDER TO HAVE an inverse.

C. e^x --- ln(y) , y>0

a^x -- log_ay , a,y>0

arcsin,etc

D.  f(f(x)) = x.

I think

f(x)=(ax+b)/(x−a)