Set, Relation and FunctionHard
Question
Let f(x) = 
, a > 0, x ≥ 0, then which of the following is/are correct ?
, a > 0, x ≥ 0, then which of the following is/are correct ?Options
A.range of f(x) is 
B.domain of f(x) is 
C.f(x) is increasing function
D.f(x) is continous in its domain
Solution
f(x) = 
, x ≥ 0, a > 0
Domain
x ∈ 
f(x) is decreasing (∵ Nr is ↓ and Dr is ↑) and continuous ( ∵ sec-1((ax + 2) ≠ 0)
⇒ Range is
i.e. 
, x ≥ 0, a > 0Domain
x ∈ f(x) is decreasing (∵ Nr is ↓ and Dr is ↑) and continuous ( ∵ sec-1((ax + 2) ≠ 0)
⇒ Range is
i.e. Create a free account to view solution
View Solution FreeMore Set, Relation and Function Questions
The set S = {1, 2, 3, ...., 12) is to be partitioned into three sets A, B, C of equal size. Thus, A∪B∪C = S,...Among 1000 families of a city, 40% read newspaper A, 20% read newspaper B, 10% read newspaper C, 5% read both A and B, 3...Which one of the following relations on R is equivalence relation -...A real valued function $f(x)$ satisfies the functional equation $f(x - y) = f(x)f(y) - f(a - x)f(a + y)$ where $a$ is a ...The domain of the function f(x) = is...