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# Show that the function $f : R \to R$ given by $f (x) = x^3$ is injective.

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Toolbox:
• A function $f: X \rightarrow Y$ where for every $x1, x2 \in X, f(x1) = f(x2) \Rightarrow x1 = x2$ is called a one-one or injective function.
Given $f : R \to R$ define by $f(x) = x^3$
A function $f: X \rightarrow Y$ where for every $x1, x2 \in X, f(x1) = f(x2) \Rightarrow x1 = x2$ is called a one-one or injective function.
Let $f(x)=f(y) \rightarrow$ $x^3=y^3$
This is possible only if $x=y \rightarrow f$ is injective.
answered Feb 27, 2013 by
edited Mar 20, 2013