QJEEM19Ma9f31: JEE Main 2019 Mathematics - Class 11 JEEM19Ma9f31 Solution: Let a function f : (0, ) (0, ) be defined by f(x) = . Then f is :

Question

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Let a function f : (0,

\infty

)

\to

(0,

\infty

) be defined by f(x) =

\left| {1 - {1 \over x}} \right|

. Then f is :

Accepted Answer

f (x) = | 1 - \frac{1}{x} | = \frac{| x - 1 |}{x} = {\begin{matrix} \frac{1 - x}{x} & 0 < x \leq 1 \\ \frac{x - 1}{x} & x \geq 1 \end{matrix}

\Rightarrow

f(x) is not injective

but range of function is

\left[ {0,\infty } \right)

Remarks : If co-domain is

\left[ {0,\infty } \right)

, then f(x) will be surjective.

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