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The typical rational function has the form p(x)/q(x) where p and q are polynomials. p(x) is called the numerator and q(x) is called the denominator. Example: In the rational function. which simplifies to simplifies to (x+2)/(x-3), but the x = 2 is NOT in the domain of g(x) whereas it IS in the domain of (x+2)/(x-3).
f (x) = (x - 1) / (x + 2) Solution to Example 7. 1  For this rational function, a direct algebraic method similar to those above is not obvious. Let us first find its inverse, the domain of its inverse which give the range of f.  We first prove that f is a one to one function and then find its inverse.