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The function f(x) is defined in [0,1]. ...

The function `f(x)` is defined in `[0,1]`. Find the domain of `f(tanx).`

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Here, `f(x)` is defined in `[0,1].`
So, `x in [0,1],` i.e., the only values of x that we can subsitute lies in `[0,1].`
For `f(tanx)` to be defined, we must have
`0 le tan x le 1 " [As x is replaced by tan x]" `
i.e., `n pi le x le n pi +(pi)/(4), n in Z " [in general]" `
Thus, the domain of `f(tanx)` is
`underset(n in Z)(cup)[n pi,n pi+(pi)/(4)]`
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