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Show that the function defined by `f(x) = | cos x |`is a continuous function. |
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Answer» Let `g(x)=cos x` and `h(x)=|x|` be two functions defined on R. Then `" (hog) (x) = h (g (x))"` `" "=h(cosx)=|cosx|` `" "=f(x)," for all " x in R` g(x) = cos x, being a cosine function, is continuous on R. h(x) = cos x, being a modulus function, is continuous on R. `therefore" "f(x)=(hog)(x)`, being a composition of two continuous functions, is continuous on R. Hence, f(x) = |cos x | is continuous function. |
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