The range of the function `f(x)=x^2+1/(x^2+1)` is

Options

A. `[1,oo)`
B. `[2,oo)`
C. `[3//2,oo)`
D. none of these

Explanation

To find the range of the function \( f(x) = \frac{x^2 + 1}{x^2 + 1} \), we will analyze the function step by step.

### Step 1: Understanding the Function
The function can be rewritten as:
\[ f(x) = \frac{x^2 + 1}{x^2 + 1} = 1 \]
This means that for any value of \( x \), \( f(x) \) is always equal to 1.

### Step 2: Determine the Range
Since \( f(x) = 1 \) for all \( x \), the output of the function does not vary with different inputs. Therefore, the range of the function is simply the set of values that \( f(x) \) can take.

### Conclusion
The range of the function \( f(x) \) is:
\[ \text{Range} = \{1\} \]