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Q.
The function $f$ : $R\to R$ defined by $f(x) = 3 - 4x$ is
Relations and Functions - Part 2
Solution:
Let $y \in R$ be any real number, such that $f(x) = y$
$\therefore y = 3 - 4x$
$\Rightarrow 4x=3-y$
$\Rightarrow x=\frac{3-y}{4}$
So, for any real number $y \in R$, there exists $\frac{3-y}{4} \in R$ such that $f \left(\frac{3-y}{4}\right)=3-4\left(\frac{3-y}{4}\right)=3-3+y=y$
Hence, $f$ is onto.