Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If the function f: [1, ∞ ) → [1, ∞ ) is defined by f(x) = 2 x(x – 1) then f –1 is
A
(1/2) x(x – 1)
B
C
D
Not defined
Text Solution
Verified by ExpertsThe correct answer is:
B
f : [1, ∞ ) → [1, ∞ )
f(x) = 2 x(x – 1)
x(x – 1) is strictly increasing in domain
f(x) = 2 x(x – 1) is one one & onto function so inverse is defined
2 x(x – 1) =y ⇒ x 2 – x = log 2 y ⇒ x 2 – x – log 2 y = 0
x = 
–ve sign rejected as domain range of f n is [1, ∞ )
f –1 (x) = 
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
The function , where assumes its minimum value only at one point, if . Find .
2. If be two fixed positive integers such that for all real , then is a periodic function with …
3. The domain of the function , where the symbols have their usual meanings, is the set . Find nu…
If , then . Find .
, then is equal to . Find .
Let and be the roots of , then is equal to Find .