If f(x) = |x|, prove that fof = f.
We have, f(x) = |x|
We assume the domain of f = R and range of f = (0,∞)
Range of f ⊂ domain of f
∴ fof exists,
Now,
fof(x) = f(f(x)) = f(|x|) = ||x|| = f(x)
∴ fof = f
Hence proved.