Question

Function $f:N \rightarrow N,f(x) = 2x + 3$ is

• A. One-one onto
• B. One-one into
• C. Many-one onto
• D. Many – one into

Answer 1

Answer: (B)

One-one into

Answer 2

$f$ is one-one because$f(x_{1}) = f(x_{2})$

$\Rightarrow 2x_{1} + 3 = 2x_{2} + 3 \Rightarrow x_{1} = x_{2}$

Further $f^{- 1}(x) = \frac{x - 3}{2} \notin N$ (domain) when x = 1, 2, 3 etc.

$\therefore$ f is into which shows that f is one-one into.