Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202421 May 2024Morning ShiftMathematicsFunctionsActual

The range of the real valued function f(x)= x^2+2 x-15 2 x^2+13 x+15 is

Options

  1. AR - -5,- 3 2
  2. BR - -5, 1 2
  3. CR - 1 2 , 8 7
  4. DR - - 3 2 , 8 7

Correct answer

C. R - 1 2 , 8 7

Step-by-step solution

aligned & x^2+2 x-15 2 x^2+13 x+15 =y & (2 y-1) x^2+(13 y-2) x+15 y+15=0 & 2 y-1 0 y 1 2 & Discriminant 0 & (13 y-2)^2-60(y+1)(2 y-1) 0 & (7 y-8)^2 0 y 8 7 y R- 1 2 , 8 7 aligned

Practice Functions on Quantrex Academy →

More from Functions

If f : R A , defined by f ( x )= x + 3 x -1 , is an onto function then A = 2025Let g(x)=1+x-[x] and f(x)= cases -1, & x 0 cases ([x] ) denotes the greatest integer less than or equal to (x ). Then for all x , f ( g ( x ))= 2025The domain of the real valued function f(x)= 3 4-x^2 + ₁₀ (x^3-x ) is 2025A real valued function f: A B defined by f(x)= 4-x^2 4+x^2 x A is a bijection. If -4 A then A B= 2025Let [ x ] represent the greatest integer less than or equal to x , x = x -[ x ] , 2 =1.414 and 3 =1.732 . If f(x)= x+ [ x 1+x^2 ] is a real valued function, then f ( 2 )+ f (- 3 )= 2025If the range of the function f(x)=-3 x-3 is 3,-6,-9,-18 , then which one of the following is not in the domain of f ? 2025The domain of the function f(x)= _e ( 1 x^2-4 x+4 ) + ⁻¹ (x^2-2 ) is 2025Consider the following statements Statement-I : A function f : A B is said to be one-one if and only if f(x) f(y) x y Statement-II : A relation f: A B is said to be a function if x 2025 Full Functions list All AP EAMCET PYQs