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Many-One onto Function

Let f:R → R...

Question

Let $f : R \to R$ be defined by i) $f (x) = x + 1$ ii) $f (x) = x + | x |$ . Determine whether or not $f$ is onto.

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Solution

Onto means in $f : R$ that range is $R$
$f (x) = x + 1$
learly x can take any value and range is $R$
Range is $R$
Function is onto
(ii) $f (x) = x + | x |$
$f x < 0$
else $x > 0$
$f (x) = 2 x$
Range is $[0, \infty)$
Not onto function

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