Given `f(x)=(x+1)^2` and `g(x)=sqrt(x)-1` ; show that `f(x) "and" g(x)` are inverses of each other.
(1) We can show that two functions are inverses by showing that `f(g(x))=g(f(x))=x`
Thus the functions are inverses.
Note that the graph of `f(x)` starts at -1; for the functions to be inverses the domain of `f` is the range of `g` , thus the domain of `f` is `x>=-1` . The domain of `g` is the range of `f` , so the domain of `g` is `x>=0` . (The additional restriction on `g` , that is that the argument of the square root be nonnegative is covered)
Note also that the graphs are symmetric about the line y=x.