1 1 vote If $f\left ( ab \right )=f\left ( a \right )f\left ( b \right )$ for all positive integers $a$ and $b$, then the largest possible value of $f\left (1\right )$ is $1$ $2$ $0$ $3$ Quantitative Aptitude cat2017-2 quantitative-aptitude functions + – go_editor 14.2k points 1.6k views answer comment Share Follow Print 0 reply Please log in or register to add a comment.
1 1 vote Given that, $f(ab)=f(a)f(b);\forall$ $a,b \in \mathbb{Z}^{+}.$ Now, $f(1\cdot1)=f(1)f(1)$ $\Rightarrow f(1)=f^{2}(1)$ $\Rightarrow f^{2}(1)-f(1)=0$ $\Rightarrow f(1)(f(1)-1)=0$ $\Rightarrow f(1)=0; f(1)=1$ $\therefore$ The largest possible value of $f(1)$ is $1.$ Correct Answer $:\text{A}$ Anjana5051 answered Dec 31, 2021 • edited Dec 31, 2021 by Lakshman Bhaiya Anjana5051 12.1k points comment Share Follow 0 reply Please log in or register to add a comment.