Let f- - - 0- be a function defined by fx - x - 1x- Then f is

Y = x 1x 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 ...

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Standard XIII

Mathematics

Many-One onto Function

Let f: ℝ - 0→...

Question

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

one-one and onto

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one-one but not onto

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onto but not one-one

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neither one-one nor onto

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Solution

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.

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Let f:R−{0}→R be a function defined by f(x)=x−1x. Then f is

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