Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202310 May 2023Evening ShiftMathematicsFunctionsActual

The domain of the function f (x)= ⁻¹ ( |x|+5 x^2+1 ) is (- ,-a] [a, ) . Then a is equal to

Options

  1. A17 2 +1
  2. B17 -1 2
  3. C1+ 17 2
  4. D17 2 -1

Correct answer

C. 1+ 17 2

Step-by-step solution

f(x)= ⁻¹ ( |x|+5 x^2+1 ) f (x) is defined, if aligned & -1 |x|+5 x^2+1 1 & 0 |x|+5 x^2+1 1 & x^2-|x|-4 0 & (|x|- 1- 17 2 ) (|x|- 1+ 17 2 ) 0 & |x| 1+ 17 2 & or |x| 1- 17 2 , which is not possible & x (- ,- 1+ 17 2 ] [ 1+ 17 2 , ) & a = 1+ 17 2 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 MHT CET PYQs