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Show that f(x)=tan^(-1)x-x is decreasing...

Show that `f(x)=tan^(-1)x-x` is decreasing function on `Rdot`

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Verified by Experts

We have given
`f(x)=tan^(-1)x-x`
Now,
`f′(x)= 1/(1+x^2)-1`
or `f′(x)= -(x^2)/(1+x^2) <=0` for all `x in R`
This gives the function f(x) is decreasing on `R`
Hence`f(x)=tan^(-1)x-x` is decreasing function on `R`
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