Show that the function f : R rightarrow R giv | vedclass

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Question

$f : R \rightarrow R$ is given as $f ( x )= x ^{3}$

For one - one

Suppose $f(x)=f(y),$ where $x, \,y \in R$

$\Rightarrow x^{3}=y^{3}$  &

Vedclass · Accepted Answer

Vedclass · Answer

$f : R ightarrow R$ is given as $f ( x )= x ^{3}$

For one - one

Suppose $f(x)=f(y),$ where $x, \,y \in R$

$\Rightarrow x^{3}=y^{3}$       ........... $(1)$

Now, we need to show that $x=y$

Suppose $x 
eq y,$ their cubes will also not be equal.

$\Rightarrow x^{3} 
eq y^{3}$

However, this will be a contradiction to $(1)$.

$	herefore  $  $x = y$ Hence, $f$ is injective.

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

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