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CGP EDU Academic Team
Published on: August 12, 2026
Which of the following functions have inverse defined on their ranges?
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(b, d)
The function in is not one-one, so f –1 is not defined. The function in is one-one and onto defined from R → R , hence f –1 is defined from R → R given by f –1 (x) = x 1/3 . The function f(x) = sin x is not one-one in (0, 2 π ) as f( π /4) = f(3 π /4) = 1/ 
, so it is not invertible. The function f(x) = e x is one-one as e x = e y ⇔ x = y. The range f = R + = {x : x > 0}. So inverse of f viz log x is defined on R + to R .
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