1.

Show that the function f defined by f (x) = |1 + x - |x|| Where x is any real number, is a continuous function.

Answer»

Solution :Define G byg (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) beinga COMPOSITE of two continuous functions is continuous.


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