AP EAMCET20224 Jul 2022Evening ShiftMathematicsFunctionsActual
x ∈ R / x 2 - 2 x - 8 log 2 - x - x 2 is a real number
Options
- A( - ∞ , - 4 ] U [ 4 , ∞ )
- Bϕ
- C- 1 , 2
- D( - ∞ , - 4 ] ∪ - 1 , 2 ∪ [ 4 , ∞ )
Correct answer
B. ϕ
Step-by-step solution
Let f x = x 2 - 2 x - 8 log 2 - x - x 2 ⇒ f x = x 2 - 2 x - 8 log - x 2 - x + 1 log - x 2 - x + 1 is defined for - x 2 - x + 1 > 0 ⇒ x 2 + x - 1 < 0 ⇒ x - - 1 + 5 2 x - - 1 - 5 2 < 0 ⇒ x ∈ - 1 - 5 2 , - 1 + 5 2 ⇒ x ∈ - 1 . 61 , 0 . 61       . . . . i And, x 2 - 2 x - 8 ≥ 0 Put x = t ⇒ t 2 - 2 t - 8 ≥ 0 ⇒ t + 2 t - 4 ≥ 0 ⇒ t ∈ ( - ∞ , - 2 ] ∪ [ 4 , ∞ ) ⇒ x ∈ ( - ∞ , - 2 ]