Question

A condition for a function $y=f\left(x\right)$ to have an inverse is that it should be

• A. defined for all $x$
• B. continuous everywhere
• C. strictly monotonic and continuous in the domain
• D. an even function

Answer 1

The correct option is C strictly monotonic and continuous in the domain

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.
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.