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) = \(\frac{3 x+1}{2 x+1}\) must be
- \(R-\left\{-\frac{1}{2}\right\}\)
- \(R-\left\{-\frac{1}{3}\right\}\)
- \(R-\left\{\frac{3}{2}\right\}\)
- R
Answer
(C) R- 3 2
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- f( x )= | x |+ x 3 x is defined for :
- Range of the function f defined by f (x) = [ 1 x ] (where [.] and . respectively denote the greatest integer…
- Complete solution set of the equation |x 2 – 1 + cos x| = |x 2 – 1| + |cos x| belonging to (–2π, π) is
- Assertion : ^ -1 x- x^ 2 2 + x^ 3 4 - = d 2 - ^ -1 x^ 2 - x^ 4 2 + x^ 6 4 for 0 Reason : ^ -1 x(x+1) + ^ -1…
- Let g ( x ) = 1 + x –[ x ] and f(x)= array cc -1, & x 0 array . then for all x, f ( g ( x )) is equal to
- Column–I Column–II (A) f (x + y) = f (x) + f (y) (P) log 3 x (B) f (xy) = f (x) + f (y) (Q) tan –1 x (C) f (x…
- The domain of the function f (x) = [4] _ 3 ( 1 | x| ) is :
- The domain of function f(x)= 1 x^ 2 - x ^ 2 , where x denotes fraction part of x .
More Sets, Relations and Functions questions · Browse all practice questions