The range of `f(x)=cos^(-1)((1+x^2)/(2x))+sqrt(2-x^2)` is (a)`{0,1+pi/2}` (b) `{0,1+pi)` `{1,1+pi/2}` (d) `{1,1+pi}`

Options

A. `{0,1+(pi)/(2)}`
B. `{0,1+pi}`
C. `{1,1+(pi)/(2)}`
D. `{1,1+pi}`

Explanation

To find the range of the function \( f(x) = \cos^{-1}\left(\frac{1+x^2}{2x}\right) + \sqrt{2 - x^2} \), we will analyze each component of the function step by step.

### Step 1: Analyze the first component \( \cos^{-1}\left(\frac{1+x^2}{2x}\right) \)

The expression \( \frac{1+x^2}{2x} \) needs to be within the domain of the \( \cos^{-1} \) function, which is defined for values between -1 and 1 (inclusive).

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