Find the range of the following functions given by
`f(x)=(3)/(2-x^(2)) " "` (ii) `f(x)=1-|x-2|`
(iii) `f(x)=|x-3| " "` (iv) `f(x)=1+3 cos 2x`

Explanation

Let's find the range of the given functions step by step.

### (i) \( f(x) = \frac{3}{2 - x^2} \)

**Step 1:** Analyze the denominator.
- The expression \( 2 - x^2 \) must not be zero, so \( x^2 \neq 2 \). This means \( x \neq \sqrt{2} \) and \( x \neq -\sqrt{2} \).

**Step 2:** Determine the behavior of \( 2 - x^2 \).
...