Published by:
CGP EDU Academic Team
Published on: August 11, 2026
Let f : R → R be a continuous function defined by f(x) = 
Statement -1 : f(c) = 
, for some c ∈ R.
Statement -2 : 0 < f(x) ≤ 
, for all x ∈ R.
Text Solution
Verified by ExpertsThe correct answer is:
D
e x + 2e –x ≥ 2 
(AM ≥ GM)
≤ 
≥ f(x) > 0 so statement- 2 is correct
As f(x) is continuous and 
belongs to range 
of f(x),
⇒ f(c) = 
for some C.
Hence correction option is .
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
Given P(x) = x 4 + ax 3 + bx 2 + cx + d such that x = 0 is the only real root of P ′ (x) = 0. If P(…
The shortest distance between the line y – x = 1 and the curve x = y 2 is
Let f : R → R be defined by
f(x) =
If f has a local minimum at x = – 1, then a possible value of k…
The equation of the tangent to the curve y = x + , that is parallel to the x-axis,
Let f be a function defined by -
f(x) =
Statement - 1 : x = 0 is point of minima of f
Statement - …
The shortest distance between line y – x = 1 and curve x = y 2 is :