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Which of the following functions is not injective ?

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$g (x) = x + \frac{1}{x}, x \in (0, \infty)$

$h (x) = x^{2} + 4 x - 5, x \in (0, \infty)$

$k (x) = e^{- x}, x \in [0, \infty)$

$f (x) = | x + 1 |, x \in [- 1, \infty)$

answer is A.

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Detailed Solution

$g (x) = x + \frac{1}{x}, x \in (0, \infty) \frac{1}{2}, 2 \in (0, \infty) g (2) = 2 + \frac{1}{2} = \frac{5}{2} g (\frac{1}{2}) = \frac{1}{2} + 2 = \frac{5}{2} 2, \frac{1}{2} h a v e s a m e i m a g e f i s n o t o n e - o n e$

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