Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
13.1k views
in Integrals calculus by (38.6k points)
edited by

Let f be a real valued function defined on (–1, 1) such that e–x f(x) = 2 + ∫√(t4 + 1) dt for t ∈ [0,x] for all x in (-1, 1) and let f –1 be the inverse function of f, then (f –1)'(2) is equal to 

(a) 1 

(b) 1/3 

(c) 1/2 

(d) 1/e

1 Answer

+2 votes
by (36.9k points)
selected by
 
Best answer

Answer is (b) 1/3

Given

when g is the inverse of f, then we shall use 

g'(y) = 1/f'(x) 

Putting y = 2 and x = 0, then 

g'(2) = 1/f'(0) = 1/3  

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...