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$_1$, x₂ ) $\in$ R such that
f(x₁) = f(x₂)
3 - 4x₁ = 3 - 4x₂
x₁ = x₂
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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