0 votes
198 views
in Sets, relations and functions by (53.8k points)

Let f : R→R, g : R→R and h : R→R be differentiable functions such that f(x) = x2 + 3x + 2, g(f(x)) = x and h(g(g(x))) = x for all x ∈R  . Then

(a)  g’(2) = 1/15

(B)  h’(1) = 666

(C)  h(0) = 16

(D)  h(g(3)) = 36

1 Answer

0 votes
by (53.5k points)
selected by
 
Best answer

Correct option (b),(c)

Explanation :

(A) It is given that f: R→R, g: R→R and h: R→R are differentiable functions.

Now, f(x) = x3 + 3x+ 2 Differentiating w.r.t. to x, we get

f '(x) = 3x2 + 2

 Also,

g(f(x)) = x

Now,

Now,

 Hence, option (A) is incorrect. 

(B) For all x  ∈ R :

Therefore, 

 Hence, option (B) is correct.

 Hence, option (D) is incorrect

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.

...