If `x in [1,2]` , then find the range of `f(x)=tanx`

Answer

`(-oo,tan 2] cup [tan 1,oo)`

Explanation

`f(x)=tanx,x in [1,2]`
Here, the limited values of x are given.
The best way to get the range of `tan x` for such values of x is graphical one.
Consider the graph of `f(x)=tanx " for " x in[1,2]`.
Clearly, from the graph, `tan in (-oo,tan 2] cup [tan 1, oo)`.