Question

Find the inverse of m(x)=√ x+1/x, x>0

Answer 1

Is it one to one though?

Answer 2

\[
\lim_{x\to 0}m(x) = \infty \\
\lim_{x\to \infty}m(x) = \infty \\

\]It's not one to one, so it doesn't have an inverse.

Answer 3

books says the answer is m^-1(x)=1/x^2-1

Answer 4

Then either you wrote the equation wrong or the book is wrong.

Answer 5

\[ \large
m^{-1}(m(x)) = \frac{1}{(\sqrt{x}-\frac{1}{x})^2}-1 \neq x
\]