Find the domain for `f(x)=sin^(-1)((1+x^2)/(2x))`

Explanation

To find the domain of the function \( f(x) = \sin^{-1}\left(\frac{1 + x^2}{2x}\right) \), we need to ensure that the argument of the inverse sine function lies within the valid range. The domain of the function \( \sin^{-1}(y) \) is defined for \( y \) in the interval \([-1, 1]\). Therefore, we need to solve the inequality:

\[ -1 \leq \frac{1 + x^2}{2x} \leq 1 \]

### Step 1: Solve the left inequality
First, we solve the left part of the inequality:
...