Set, Relation and FunctionHard
Question
If domain & range of function f(x) = 
are same, where a,b ∈ R & b > a, then -
are same, where a,b ∈ R & b > a, then -Options
A.a = - 1 + √2, b = 2 - √2
B.a = 1 + √2, b = 2 - √2
C.a = - 1 - √2, b = 2 + √2
D.a = - 1 + √3, b = 2 - √3
Solution
Domain of f(x) is [a,b]
f′(x) =
= 0 ⇒ x = 
f(a) = f(b) =
& f
= √2
range is
⇒ b - a = a2 & 2(b - a)= b2
∵ a ≠ b
∴ (b2 - a2) = (b - a) ⇒ a + b = 1
⇒ a2 + 2a - 1 = 0
⇒ a = - 1 - √2 & b = 2 + √2 or a = - 1 + √2 & b = 2 - √2
f′(x) =
= 0 ⇒ x = f(a) = f(b) =
& f = √2range is
⇒ b - a = a2 & 2(b - a)= b2
∵ a ≠ b
∴ (b2 - a2) = (b - a) ⇒ a + b = 1
⇒ a2 + 2a - 1 = 0
⇒ a = - 1 - √2 & b = 2 + √2 or a = - 1 + √2 & b = 2 - √2
Create a free account to view solution
View Solution FreeMore Set, Relation and Function Questions
Let g : → be a differentiable functions with g(0) = 0, g′(0) = 0 and g′(1) ≠ 0. Let and h(x) = e...Let A = {2, 3, 4, 5} and let R = {(2, 2), (3, 3), (4, 4), (5, 5), (2, 3), (3, 2), (3, 5), (5, 3)} be a relation on A. Th...If 0 ≤ [x] < 2 , - 1 ≤ [y] < 1 and 1 ≤ [z] < 3 where [·] denotes the greatest integer functio...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,...Let f : (-1, 1) → B, be a function defined by f(x) = tan-1 , then f is both one-one and onto when B is the interva...