If `g(x)` is a decreasing function on `R` and `f(x)=tan^(-1){g(x)}` . State whether `f(x)` is increasing or decreasing on `R` .

Explanation

We have,

`f(x)=tan ^{-1}[g(x)]`

g(x) is a decreasing function
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therefore g^{prime}(x)<0 forall x in R`
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f^{prime}(x)=frac{1}{1+g^{2}(x)} times g^{prime}(x)`
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