Question

# Show that the function f Defined by f(x)=|1-x+|x|| is a continuous  function

Solution

## f(x) = |1-x+|x|| Consider the function, g(x)=1-x+|x| and h(x)=|x|, Then..take composition (h o g)(x)= h(g(x))                 = h(1-x+|x|)                 = |1-x+|x|| Now, h(x)=|x| is continuous because modulus function is continuous. g(x)= 1-x+|x| Since (1-x) is polynomial it is continuous because polynomial functions are continuous, and |x| is continuous. Since the sum of two continuous functions is continuous, g(x)= 1-x+|x| is continuous.  hence g(x) and f(x) both are continuous.So the composition of two continuous functions are also continuous. So, f(x)= |1-x+|x|| is continuous.

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