Inverse of elementary functions

Question

which may be two right inverse of:

1) $h:\Re \rightarrow [0,\infty) $ defined by $h(x)=|x|$

2) $k:\Re \rightarrow [1,\infty)$ defined by $k(x)= e^{x^2}$

Answer 1

1). The inverse is $h^{-1}(x)=x$

2). The inverse is $k^{-1}(x)=\sqrt{\ln x}$