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Relations and Functions — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSRelations and Functions1 Mark
Question
Show that the function $f : R \rightarrow R$ given by $f(x) = x^3$ is injective.
✓

Answer

Let $x_1, x_2 \in R$ be such that $f(x_1) = f(x_2)$
$ \Rightarrow x_1^3 = x_2^3$
$\Rightarrow x_1 = x_2$
Therefore$, f$ is one$-$one function,
hence $f(x) = x^3$ is injective.

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