Question

Every invertible function is

• A. monotonic function
• B. identity function
• C. constant function
• D. not necessarily monotonic

Answer 1

The correct option is A monotonic function

For a function to have its inverse in a given domain, it should be continuous in that domain and should be a one-one function in that domain.
If the function is one-one in the domain, then it has to be strictly monotonic.
Hence an invertible function is
$\to$ monotonic and
$\to$ continuous.
For example $y=sin\left(x\right)$ has its domain in $xϵ[-\frac{\pi }{2},\frac{\pi }{2}]$ since it is strictly monotonic and continuous in that domain.