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

Explanation

To find the domain of the function \( f(\tan x) \) where \( f(x) \) is defined in the interval \([0, 1]\), we need to ensure that the output of \( \tan x \) falls within this interval. Here’s how to solve it step by step:

### Step 1: Identify the range of \( \tan x \)
The function \( \tan x \) is defined for all \( x \) except for odd multiples of \( \frac{\pi}{2} \). The range of \( \tan x \) is all real numbers, but we are interested in the values that fall within the interval \([0, 1]\).

### Step 2: Set up the inequality
We need to find the values of \( x \) such that:
\[
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