 xf(1),$ so $f(x) = 25x.$  In particular, $f(79) = \boxed{1975}.$The answer is: 1975
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
The function $f(x)$ satisfies
\[f(xy) = xf(y)\]for all real numbers $x$ and $y.$  If $f(1) = 25,$ find $f(79).$

### Answer:
