I need answers to these questions plz!

Question

1.) For what domain are f(x)=x^2 and g(x)=(square root) x inverse functions? Use builder notation.

2.)Explain how you can tell that f(x)=x^3 and g(x)=(smaller 3 with square root) x are inverse functions. Use complete sentences.

3.) list two more functions that are inverses of each other.

4.) list a function besides f(x)=-x, f(x)=1/x, or f(x)=-1/x this is its own inverse.

Answer 1

g(x)=x^1/2 is not defined for x<0

f(x)=x² and g(x)=x^1/2 are inverses for x in [0,∞).

Other common inverses: sin/arcin and e^x/ln x.

Any function the graph of which is symmetric tom y=x will be its own inverse:

f(x)=(1-x²)^1/2 for x in [0,1], f(x)=-x both are self inverses.