Question

Let $f:R-\left\{0\right\}\to R$ be a function defined by $f\left(x\right)=x-\frac{1}{x}.$ Then $f$ is

• A. one-one and onto
• B. one-one but not onto
• C. onto but not one-one
• D. neither one-one nor onto

Answer 1

The correct option is C onto but not one-one

$y=x-\frac{1}{x}$

Clearly, the given function attains all the values of its co-domain, the real set $R$ and hence it is an onto function.

Also, if we draw a horizontal line parallel to $x$-axis, it cuts the graph of the given function in more than one point and hence it is a many-one function.