If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(1) is

Question

Accepted Answer

1 — Easy Substitute $a=b=1$ into the functional equation. This forces a simple equation in $f(1)$ alone, whose largest solution is the answer. 1 Plug in $a=b=1$. Then $ab=1$, so the relation $f(ab)=f(a)f(b)$ becomes an equation in $f(1)$. Let $x=f(1)$. $$\begin{aligned} &f(1\cdot 1)=f(1)\,f(1)\ &\Rightarrow\ x=x\cdot x\ &\Rightarrow\ x^2-x=0 \end{aligned}$$ 2 Solve for $x$. Factor. $$\begin{aligned} &x(x-1)=0\ &\Rightarrow\ x=0\quad	ext{or}\quad x=1 \end{aligned}$$ The largest possible value of

CAT 2017 Slot 2 — QA Question 31

Answer & solution

Related Basics (Functions) questions