Q. 25.0( 1 Vote )

Mark the correct alternative in each of the following:

f: R R given by is

A. injective B. surjective

C. bijective D. none of these

Answer :

Given function is f: R R given


f(x) = x + √x2


For this function if we take x = 2,


f(x) = 2 + √4


f(x) =2


For this function if we take x = -2,


f(x) = -2 + √4


f(x) = 0


So, in general for every negative x, f(x) will be always 0. There is no x ϵ R for which f(x) ϵ (-∞, 0).


Hence, it is neither injective nor surjective and so it is not bijective either.

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