Relations and Functions — Practice Questions

If the function f: (-∞, -1) → (a, b) defined by f(x) = e^(x³ - 3x + 1) is one-one and onto, then the distance of the point P(2b + 4, a + 2) from the line x + e⁻³y = 4 is:

Let A = {1, 2, 3, ...100}. Let R be a relation on A defined by (x, y) ∈ R if and only if 2x = 3y. Let R₁ be a symmetric relation on A such that R ⊂ R₁ and the number of elements in R₁ is n. Then the minimum value of n is _______.

The real valued function f(x) = cosec⁻¹x/√(x-[x]), where [x] denotes the greatest integer less than or equal to x, is defined for all x belonging to:

If the functions are defined as f(x) = √x and g(x) = √(1-x), then what is the common domain of the following functions: f + g, f - g, f/g, g/f, g - f, where (f ± g)(x) = f(x) ± g(x), (f/g)(x) = f(x)/g(x)