Inverse of a function

Question

1.) For what domain are f(x)=x^2 and g(x)=√x inverse functions? Make sure you use set builder notation.

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

3.) List two more functions that are inverse of each other.

4.) List a function besides f(x)=-x, f(x)=x, f(x)=1/x, or f(x)=-1/x that is it’s own inverse.

Answer 1

I don't know what "set builder" notation is, but x² and √x are inverses for x≥0.

The graph of a function and its inverse are symmetric with respect to the line y=x; a graph showing y=x³ and y=x^1/3 will show that these two functions are inverses for all real x.

1/x is the inverse of 1/x.

e^x and ln x are inverses for x>0

Any straight line perpendicular to y=x will be symmetric to y=x and thus the function representing such a line will be its own inverse, e.g. y=f(x)=1-x.