Join Sarthaks eConnect Today - Largest Online Education Community!
0 votes
asked in Mathematics by (63.3k points)

Let g be the inverse of the continuous function f, Let there be a point (αβ), where α  β, is such that it satisfies each of y = f(x) and y = g(x) then

(A) the equation f(x) = g(x) has infinitely many solutions 

(B) the equation f(x) = g(x) has at least 3 solutions

(C) f must be a decreasing function of x

(D) g can be an increasing function of x

1 Answer

+1 vote
answered by (68.5k points)
selected by
Best answer

Correct option  (B)(C)


As the point (α , β), lies on both f(x) and g(x) , the point (β,α) will also lie on both the curves and as the functions are continuous they must cross (meet on) the line y = x in between. f must be on decreasing path, for all these to happen.

Happy Diwali Wishes

Related questions

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.

One Thought Forever

“There is a close connection between getting up in the world and getting up in the morning.“
– Anon