UPSC NDA I 2025 Mathematics Paper

Given,
The function is such that: f(xy)=f(x+y) for all real values of x and y, and f(5)=10.
We need to find the value of f(0).
Substitute x=5 and y=0 in the given functional equation f(xy)=f(x+y) :
‌f(5⋅0)=f(5+0)
‌f(0)=f(5)
Since f(5)=10, we conclude:
f(0)=10