Let f : R → R be defined as f(x) = x4. Choose the correct answer.

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KollegeApply · Accepted Answer

f is neither one-one nor onto. Explanation: f : R $\to$ R is defined as f(x) = x4 Let x, y ∈ R such that f(x) = f(y). $\Rightarrow$ x4 = y4 $\Rightarrow$ x = $\pm$y $\therefore$ f(x1) = f(x2) does not imply that x1 = x2. For instance, f(1) = f(–1) = 1 $\therefore$ f is not one-one. Consider an element 2 in co-domain R. It is clear that there does not exist any x in domain R such that f(x) = 2. $\therefore$ f is not onto. Hence, function f is neither one-one nor onto.

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