Solution Define g by g(x) = 1 – x + |x| and  h by h(x) = |x| for all real x Then
(h o g) (x) = h (g (x))
= h (1– x + |x |)
= |1– x + | x|| = f (x)
In Example 7, we have seen that h is a continuous function Hence g being a sum
of a polynomial function and the modulus function is continuous But then f  being a
composite of two continuous functions is continuous