If f(x)=1/(x^2+1) and g(x)=x^2/(x^2+1), what is (f+g)(x)?

Correct answer: 1

The sum of two functions is found by adding their values at the same input. Here both fractions have the common denominator \\(x^2+1\\), so their numerators can be added while the denominator remains unchanged. Thus, the operation is direct and no separate domain problem appears because \\(x^2+1\\) is always positive for every real number \\(x\\). This makes option A the appropriate simplified result.

Using the definitions, \\( (f+g)(x)=f(x)+g(x)=\\frac{1}{x^2+1}+\\frac{x^2}{x^2+1} \\). Combining the numerators gives \\(\\frac{1+x^2}{x^2+1}\\). Since the numerator and denominator are the same expression, the fraction equals \\(1\\). Option B incorrectly adds an extra 1 to the numerator, while option C uses subtraction. Therefore, A follows.