Function Questions

For every pair of continuous functions f, g : [0, 1] →R  such that max {f(x) : x ∈ [0, 1]} = max {g(x) : x ∈ [0, 1]}, the correct statement(s) is(are) :

Let f: → R be given by f(x) = (log(secx + tanx))3. Then

Let f : (0, ∞) → R be given by f(x) = . Then

Let [x] be the greatest integer less than or equals to x. Then, at which of the following point(s) the function f(x)=x cos(π(x + [x])) is discontinuous ?...

Let f: R → R be a positive increasing function with = 1. Then =...

Let f be a real-valued function defined on the interval (- 1, 1) such that e-xf(x) = 2 + dt, for all x ∈ (-1, 1) and let f-1 be the inverse function of f. Then (f-1)′ (2) is equal to...

[cot x]dx, [•] denotes the greatest integer function, is equal to

Let y be an implicit function of x defined by x2x - 2xx cot y - 1 = 0. Then y′(1) equals

Let y be an implicit function of x defined by x2x - 2xx cot y - 1 = 0. Then y′(1) equals

The largest interval lying in for which the function is defined, is...

A value of C for which the conclusion of Mean Value Theorem holds for the function f(x) = logex on the interval [1, 3] is

Let f : R → R be a function defined by f(x) = Min {x + 1, |x| + 1}. Then which of the following is true?

The function f: R ~ {0} → R given by f(x) = can be made continuous at x = 0 by defining f(0) as

The function f(x) = has a local minimum at

Let f : R → R be a differentiable function having f(2) = 6, f′(2). Then dt equals...

The graph of the function y = f(x) is symmetrical about the line x = 2, then

The function f(x) = log (x +, is

Maximum value of function f(x) = ∀ x ∈ R is

Let f : (4, 6) → (6,8) be a function defined by f(x) = x + . (where [.] denotes the greatest integer function) , then f-1 (x) is euqal to :-...

is equal to :- (where [.] greatest integer function)