List of top Mathematics Questions on Function asked in Tripura JEE

If $ f(x) $ and $ g(x) $ are two functions such that $ f(x) + g(x) = e^x $ and $ f(x) - g(x) = e^{-x} $, then:
The mapping $ f: \mathbb{R} \to \mathbb{R} $ such that $ f(x) = |x - 1| $, $ x \in \mathbb{R} $ is: