Prove that the function f: R R, given by f(x) = 2x, is one-one an… - Vidyadip

Question

Prove that the function $f: R \rightarrow R,$ given by $f(x) = 2x,$ is one$-$one and onto.

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Answer

$x_1 ,x_2$ are two different elements of $R$
Let $f(x_1) = f (x_{2})$
$2x_1= 2x_2$
$x_1 = x_{2,}$hence $f$ is one$-$one.

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