Question

Prove that the function $f:N\to N$ defined by $f\left(x\right)=2x-1$ is one-to-one. [2 marks]

Answer 1

Suppose $f\left(a\right)=f\left(b\right)$ for $a,b\in N.$
$\Rightarrow 2a-1=2b-1$
$\Rightarrow a=b$ [1 mark]
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. [1 mark]