Question

Which condition represents a one-one (injective) function?

Options

• \(x_1\ne x_2\text{ but }f(x_1)=f(x_2)\)

• \(\text{Range}\subset\text{Codomain}\)

• \(f(x_1)=f(x_2)\Rightarrow x_1=x_2\)

• \(\text{Range}=\text{Codomain}\)

Answer 1

The one-one condition states that equal outputs must come from equal inputs. Thus, \[f(x_1)=f(x_2)\Rightarrow x_1=x_2\] expresses different inputs leading to different outputs.