Q. 25.0( 1 Vote )

# Mark the correct alternative in each of the following:f: R → R given by isA. injective B. surjectiveC. bijective D. none of these

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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