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.
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