Let A = {x R: x is not a positive integer}. Define a function f: A → R as f (x) = , then f is

Engineering

Mathematics

Types of Functions

Question

Let A = {x $\in$ R: x is not a positive integer}. Define a function f: A → R as f (x) = $\frac{2 x}{x - 1}$ , then f is

Injective but not surjective

Neither injective nor surjective

Not injective

Surjective but not injective

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$f (x) = 2 (1 + \frac{1}{x - 1})$

$f' (x) = \frac{2}{{(x - 1)}^{2}}$

⇒ of is one – one but not onto