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Show that the function f defined by f(x)...

Show that the function `f` defined by `f(x)=|1-x+|x||` is everywhere continuous.

Text Solution

Verified by Experts

Define g by g (x) = 1 + x - |x|
h by h(x) = |x|, then
(hog) (x) = h(g(x))
h ( 1+ x - |x|)
= | 1 + x - |x|| = f(x)
h(x) is a continuous function. Hence g being a sum of a polynomial function and modulus function is continuous . But then f(x) being a composite of two continuous functions is continuous.
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