## Calculus: Early Transcendentals 8th Edition

The functions $f(x)$ and $g(u)$ are equivalent because they are the same function with different variables ($f$ gives the result in terms of $x$, while $g$ gives it in terms of $u$). Denoting the variable with a different letter does not change the function. To put it in other words, the two functions give the same output for the same input.