NIMCET 2010 — Mathematics PYQ
NIMCET | Mathematics | 2010Let f(x)=1−x1+x+31. Then the domain of the real function f is:
Choose the correct answer:
- A.
(−∞,−3)∪(1,∞)
- B.
(1,∞)
- C.
(−∞,1)∩(−3,∞)
(Correct Answer) - D.
x=1,x=−3
(−∞,1)∩(−3,∞)
Explanation
1. For the first term 1−x1:
1 - x > 0
1 > x
x < 1 \implies x \in (-\infty, 1)
2. For the second term x+31:
x + 3 > 0
x > -3 \implies x \in (-3, \infty)
3. Common Domain (Intersection):
The function f(x) is defined only where both terms are defined.
Domain=(−∞,1)∩(−3,∞)
Equivalently, this can be written as:
-3 < x < 1 \quad \text{or} \quad (-3, 1)
Correct Option:
(c) (−∞,1)∩(−3,∞)
Explanation
1. For the first term 1−x1:
1 - x > 0
1 > x
x < 1 \implies x \in (-\infty, 1)
2. For the second term x+31:
x + 3 > 0
x > -3 \implies x \in (-3, \infty)
3. Common Domain (Intersection):
The function f(x) is defined only where both terms are defined.
Domain=(−∞,1)∩(−3,∞)
Equivalently, this can be written as:
-3 < x < 1 \quad \text{or} \quad (-3, 1)
Correct Option:
(c) (−∞,1)∩(−3,∞)