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 ?...

If f : R → R is a function defined by f(x) = [x] cos , where [x] denotes the greatest integer function, then f is :...

Let f : [-1, 2] → [0, ∞) be a continuous function such that f(x) = f (1 - x) for all x ε [-1, 2]. Let R4 f(x)dx, and R2 be the area of the region bounded by y = f(x), x = -1, x = 2, a...

Let f(x) = x2 and g(x) = sinx for all xε R. Then the set of all x satisfying (f o g o g o f ) (x) = (g o g o f ) (x), where (f o g) (x) = f (g(x)), is

Let f(x) = , then f is

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...

Let f(x) = | x - 1|. Then

If f(x) = cos (log x ), then f(x).f(y) has the value

The domain of definition of the function y = is

Which of the following functions is periodic ?

For real x, the function will assume all real values provided.

If g {f(x)} =| sin x | and f{g(x)} = (sin √x)2, then

If f(x) = 3x - 5, then f-1(x)

If the function f : [1, ∞) → [1, ∞) is defined by f(x) = 2x(x - 1), the f -1(x)

Let f(θ) = sin θ (sin θ + sin 3 θ). The f (θ)

The domain of definition of the function y (x) is given by the equation 2x + 2y = 2, is