The ReLU activation function can assume all values in the range \( \left[0,\infty\right] \). As a remainder, its formula is
$$ \textrm{ReLU}\left(x\right) = \max\left(0,x\right). $$This choice is good when the input observations \(\mathbf{x}_{i}\) assume a wide range of positive values. If the input \( \mathbf{x}_{i} \) can assume negative values, the ReLU is, of course, a terrible choice, and the identity function is a much better choice. It is then common to replace to the ReLU with the so-called Leaky ReLu or just modified ReLU.
The ReLU activation function for the output layer is well suited for cases when the input observations \(\mathbf{x}_{i}\) assume a wide range of positive real values.