Q) The domain of the function fx=2-x3-x is A (- 3, 3) B (- 2, 2) C - Maths - Relations and Functions

Question

Q) The domain of the function f x = 2 - x 3 - x is
A (- 3, 3)
B (- 2, 2)
C - ∞ , - 3 ∪ 2 ,   2 ∪ [ 3 ,   ∞
)
D - ∞ , - 3 ∪ 2 ,   2 ∪ ( 3 ,   ∞
)

Aarushi Mishra · Accepted Answer

fx=2-x3-xLet t=x, where t>0fx=2-t3-tQuantity inside square root should be non-negative2-t3-t≥0t-2t-3≥0Drawing wavy curve

t∈(-∞,2]∪3,∞x∈(-∞,2]∪3,∞x≤2 or x>3-2≤x≤2 or x>3 or x<-3x∈-2,2∪-∞,3∪3,∞Domain=-∞,-3∪-2,2∪3,∞

Q). The domain of the function f x = 2 - x 3 - x is A. (- 3, 3) B. (- 2, 2) C. - ∞ , - 3 ∪ 2 , 2 ∪ [ 3 , ∞ ) D. - ∞ , - 3 ∪ 2 , 2 ∪ ( 3 , ∞ )