[SOLVED by @eliassaab] Define a function \(f: \mathbb{Z}^+ \longrightarrow \mathbb{Z}^+\) such that \(f\) is strictly increasing, \(f\) is multiplicative, and \(f(2)=2\). Show that \(f(n)=n\) for all \(n\).

Hey! We 've verified this expert answer for you, click below to unlock the details :)

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

f'(a) > 0
f(a)f(b) = f(ab)
f(2) = 2

\[f(2) = f(1 \times 2) = f(1)f(2)\]
hence f(1) = 1

Be careful with your derivatives. This is not a continuous function.

Looking for something else?

Not the answer you are looking for? Search for more explanations.