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

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