Question

If function $f$ has an inverse, then which of the following conditions is necessary and sufficient

• A. $f$ is a one-one function.
• B. $f$ is an onto function.
• C. $f$ is a one-one and onto function.
• D. $f$ is an identity function.

Answer 1

The correct option is C $f$ is a one-one and onto function.

To have an inverse for the function $f$, $f$ should be one-one and onto.
Each point in the domain should have a unique image in range.
So, it should be one-one.
And if it is not onto, then there will be no pre-image of the extra element, so inverse will not be possible.