Question

The function $f:N\to N$ defined by $f\left(x\right)=2x-1$ is one-to-one.

• A. False
• B. True

Answer 1

The correct option is B True

Suppose $f\left(a\right)=f\left(b\right)$ for $a,b\in N.$
$\Rightarrow 2a-1=2b-1$
$\Rightarrow a=b$
i.e., $f\left(a\right)=f\left(b\right)\Rightarrow a=b\forall a,b\in N$
Thus, the function $f$ is one-to-one.