Question

The function \(f:\mathbb{N}\to\mathbb{N}\) defined by \(f(x)=5x\) is:

Options

• Injective but not a surjection

• A surjection but not injective

• Both injective and a surjection

• Neither injective nor a surjection

Answer 1

Since \[5x_1=5x_2\Rightarrow x_1=x_2\], the function is injective. Its range consists of multiples of 5, which is not all of \(\mathbb{N}\), so it is not a surjection.