Define Rational Function Define Rational Function In mathematics, a rational function is any function which can be written as the ratio of two polynomial functions. Neither the coefficients of the polynomials nor the values taken by the function are necessarily rational numbers. We study different types of Functions in mathematics like quadratic, linear etc. and Rational Function is one of them. Here we will define rational function. A function that contains two Polynomials in fraction form or written in ratios is known as rational functions. Let's see mathematical representation of rational function. In case of polynomial with one variable 'a' is said to be rational function if and only if it is written in given form: => f (a) = U (a) / V (a), here both 'U' and 'V' both are Polynomial Functions in 'a' and value of 'V' is not zero. Here Domain of function (f) can be defined as Set of all points of 'a' for which value of denominator is not zero.
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Each polynomial function can follow property of a rational function with V (a) = 1. If a function is written in form of f (a) = sin (a) then this is not a rational function. Example of rational function is x + 1 / x2 – 1. Example : g(a) = a3 – a The function 'a' is said to be rational function only if it can be written as, g(a) = R(a) / S(a) where R and S are polynomial Functions in a and S is not zero polynomial. The Set of all points ‘a’ for which the denominator S(a) is not zero comes under the Domain of g. One can assume that this rational function is written in its lowest degree i.e. R and S have many positive degree. Polynomial functions with S(a) = 1, is said to be rational functions. Functions that can be written in this form are not rational functions. Ex : g(a) = sin(a) , is not a rational function. It is not necessary that ‘a’ need to be variable. Example: The rational function g(a) = is defined at a2 = 6 a = . The rational function g(a) = (a2 + 3) / a2 + 1 can’t be defined for the complex numbers but can be defined for Real Numbers.
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If value of a is a Square root of -1then it Mean the evaluation leads to division by zero. g(b) = (b2 + 2) / (b2 + 1) = (-1 + 3) /(-1 + 1) = 2/ 0, which is undefined. z
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