Set, Relation and FunctionHard
Question
Let p(x) be a function defined on R such that p′(x) = p′(1 - x), for all x ∈ [0, 1], p(0) = 1 and p(1) = 41. Then 
dx equals
dx equalsOptions
A.21
B.41
C.42
D.
Solution
p′(x) = p′(1 - x)
⇒ p(x) = - p(1 - x) + c
at x = 0
p(0) = - p (1) + c ⇒ 42 = c
now p(x) = - p(1 - x) + 42
⇒ p(x) + p(1 - x) = 42
2I =
⇒ I = 21
⇒ p(x) = - p(1 - x) + c
at x = 0
p(0) = - p (1) + c ⇒ 42 = c
now p(x) = - p(1 - x) + 42
⇒ p(x) + p(1 - x) = 42
2I =
⇒ I = 21Create a free account to view solution
View Solution FreeMore Set, Relation and Function Questions
The largest value of r for which the region represented by the set {ω ∈ C/|ω − 4 − i|≤...If f(x) = (where [.] and {.} represent greatest integer and fractional part function respectively), then -...Let S be a non empty subset of N. Negation of the statement ″There exists a number x∈S such that x is even&#...Consider two sets A = {1,2,3} & B = {1,2,3,4,5}. A number is selected each from set A & set B. Let p denotes the probabi...Which of the following statement(s) is/are correct about continuous functions y = f(x) & y = g(x) ?...