FunctionHard
Question
If f :[1, ∞) → [2, ∞) is given by f(x) = x + 
, then f-1(x) equals
, then f-1(x) equalsOptions
A.
B.
C.
D.
Solution
Let y = x + ⇒ y = 
⇒ xy = x2 + 1
⇒ x2 - xy + 1 = 0
⇒
⇒
⇒
Since, the range of the inverse function is [1, ∞), then
we take
If we conside
, then
f -1(x) > 1
This is possible only if (x - 2)2 > x2 - 4
⇒ x2 + 4 - 4x2 - 4
⇒ 8 > 4x
⇒ x < 2, where x > 2
Therefore, (a ) is the answer.
⇒ y = ⇒ xy = x2 + 1
⇒ x2 - xy + 1 = 0
⇒
⇒
⇒
Since, the range of the inverse function is [1, ∞), then
we take
If we conside
, then f -1(x) > 1
This is possible only if (x - 2)2 > x2 - 4
⇒ x2 + 4 - 4x2 - 4
⇒ 8 > 4x
⇒ x < 2, where x > 2
Therefore, (a ) is the answer.
Create a free account to view solution
View Solution FreeMore Function Questions
If y = f(x) satisfies the condition f(x + 1/x) = x2 + 1/x2 (x ≠ 0), then f(x) is equal to...The function f(x) = log (x +, is...Which of the following function is onto ?...Consider the function g(x) defined as g(x) (x(22011-1)-1) = (x + 1)(x2 + 1)(x4 + 1) . . .. (x22010 + 1) - 1, (|x| ≠...If S is the set of all real x such that is positive, then S contains...