Definition, Domain

The definition of a rational function is: it can be written as a ratio of two polynomials.

1. Suppose f(x) = 1/x and g(x) = 1/(x + 1). Are f(x) and g(x) both rational functions?

2. Is h(x) = f(x) + g(x) from problem 1 above a rational function? Explain.

3. What is the domain of f(x) = 1/x?

4. What is the domain of the rational function f(x) = (x – 1) / (x^{2} + 1) ?

5. What is the domain of h(x) = 1/x + 1/(x + 1)?