An algebra problem by Sumukh Bansal

Algebra Level 2

Let function $f$ be defined as:

$\large f(xy) = f(x+y)$

If $f(8) = 32$ , find $f(9)$ .

2 solutions

Zach Abueg
Sep 23, 2017

Let $x \in \mathbb{R}$ and $y = 0$ . Then

$\begin{aligned} f(x \cdot 0) & = f(x + 0) \\ \implies f(x) & = f(0) \end{aligned}$

meaning $f(x)$ is a constant function. Thus, $f(9) = f(8) = \boxed{32}$

Sumukh Bansal
Sep 21, 2017