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