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Show that the function defined b y f(x)=...

Show that the function defined b y `f(x)=|cos x|` is continous function.

Text Solution

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Let `g(x) =cos x and h (x) =|x|` be two functions defined on R. Then (hog) `(x)=h(g(x))`
` =h(cos x)=|cosx|`
`=f (x), "for all" x inR`
`g(x)=cos, x` being a cosine function, is continous on R.
Also, `h(x)=|x|,` being a modulus function, is continous on R.
`therefroe f(x)=(hog)(c),` being a composition of two continous functions, is continous on R.
Hence, `f(x)=|cosx|` is continous function.
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