If a function `F: RrarrR` is defined as `f(x)=int(x^8+4)/(x^4-2x^2+2)dx` f (0) =1 , then which of the following is correct ?

Options

A. f (x) is an even function
B. f (x) is an onto function
C. f (x) is an odd function
D. f (x) is an many one function

Answer

To solve the problem, we need to analyze the function \( f(x) = \int \frac{x^8 + 4}{x^4 - 2x^2 + 2} \, dx \) and determine its properties based on the given options.

### Step 1: Simplifying the Integral

We start with the integral:

\[ f(x) = \int \frac{x^8 + 4}{x^4 - 2x^2 + 2} \, dx \]

To simplify this, we can rewrite the numerator \( x^8 + 4 \) in a way that relates to the denominator \( x^4 - 2x^2 + 2 \).