A rational function is defined as quotient of two polynomials, p( x ) and q( x ). The…
Mathematics · JEE Advanced · NTA Exams — Sets, Relations and Functions
A rational function is defined as quotient of two polynomials, p(x) and q(x). The domain of the rational function must be all reals except the roots of the equation q(x) = 0 . The range of rational function can be found by finding minimum and maximum values of the function. In case p(x) and q(x) have a common factor x – β. Then after cancelling the common factor, the rational function must assume a value at x = β which should be deleted from the found range since β is not there in the domain of the rational function.
The range of the rational function f (x) = \(\frac{(2 \mathrm{x}+1)}{2 \mathrm{x}^{2}+5 \mathrm{x}+2}\) must be
- R – {0}
- R – {–2}
- R – {0, –2}
- \(R-\left\{0, \frac{2}{3}\right\}\)
Answer
(D) R- 0, 2 3
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