Classify the following functions as injection, surjection or bije… - Vidyadip

Question

Classify the following functions as injection, surjection or bijection:
f : R → R, defined by f(x) = |x|

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Answer

f : R → R, given by f(x) = |x|
Injectivity: Let $\text{x, y}\in\text{R}$ such that
x = y but if y = -x
⇒ |x| = |y| ⇒ |y| = |-x| = x
$\therefore$ f is not one-one.
Surjective: Since f attains only positive values, for negative real numbers in R, there is no pre-image in domain R.
$\therefore$ f is not onto.

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