State whether the function is one-one, onto or bijective. Justify… - Vidyadip

Question

State whether the function is one-one, onto or bijective. Justify your answer. $f: R \rightarrow R$ defined by $f(x) = 3 - 4x.$

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Answer

Let $\left(\mathrm{x}_1, \mathrm{x}_2\right) \in R$ such that
$f\left(x_1\right)=f\left(x_2\right) $
$ 3-4 x_1=3-4 x_2 $
$ x_1=x_2$
Hence one-one
$ \mathrm{Y}=3-4 \mathrm{x} $
$ x=\left(\frac{3-y}{4}\right) $
$ f\left(\frac{3-y}{4}\right)=3-4\left(\frac{3-y}{4}\right) $
$ \mathrm{f}(\mathrm{x})=\mathrm{y} $
$ =\mathrm{y}$
Hence onto also.

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