AP EAMCET20224 Jul 2022Morning ShiftMathematicsFunctionsActual
If f x = 2 - x 2 and g x = ln 1 - x are two real valued functions then the domain of the function f + g x is
Options
- A- 2 , 2
- B− 2 , 1
- C- ∞ , 1
- D1 , 2
Correct answer
B. − 2 , 1
Step-by-step solution
Given f x = 2 - x 2 and g x = ln 1 - x f + g x = f x + g x = 2 - x 2 + ln 1 - x Let domain of f x = 2 - x 2 be D 1 , then 2 - x 2 ≥ 0 ⇒ x 2 - 2 ≤ 0 i.e. D 1 ≡ - 2 , 2 Let domain of g x = ln 1 - x be D 2 then 1 - x > 0 ⇒ x - 1 < 0 i.e. D 2 ≡ - ∞ , 1 Hence, domain of f x + g x will be D 1 ∩ D 2 ≡ [ - 2 , 1 )