Q. 185.0( 1 Vote )
If f: R → (0, 2) defined by
is invertible, find f-1.
Answer :
We have f: R → (0, 2) and
Given that f-1 exists.
Let y ϵ (0, 2) such that f(x) = y
⇒ 2e2x = y (e2x + 1)
⇒ 2e2x = e2xy + y
⇒ 2e2x – e2xy = y
⇒ e2x (2 – y) = y
Taking ln on both sides, we get
We have f(x) = y ⇒ x = f-1(y)
But, we found f(x) = y ⇒
Hence,
Thus,
Rate this question :
How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Functions - 0152 mins
Functions - 1047 mins
Functions - 0558 mins
Functions - 0748 mins
Inverse Trigonometric Functions - 0161 mins
Range of Functions58 mins
Functions - 0253 mins
Functions - 0361 mins
Functions - 0840 mins
Functions - 1252 mins




















Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
view all courses
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation


RELATED QUESTIONS :
Let f :R → R be given by f (x) = tan x. Then f–1 (1) is
Mathematics - Exemplar| Let * be a binary operation on Q defined by
Show that * is commutative as well as associative. Also find its identity elements, if it exists.
Mathematics - Board PapersFind the identity element in the set Q + of all positive rational numbers for the operation * defined by for all a, b ∈ Q +.
Let f : A → B and g : B → C be the bijective functions. Then (g o f)–1 is
Mathematics - Exemplar