Check whether the relation S in the set of real numbers R defined by S = {(a, b) : where a – b + √2 is an irrational number} is reflexive, symmetric or transitive.

Question

TextBijective FunctionCBSE PYQ

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A function f : R+ → R (where R+ is the set of all non-negative real numbers) defined by f(x) = 4x + 3 is :

Let f : R+ → [– 5, ∞) be defined as f(x) = 9x² + 6x – 5, where R+ is the set of all non-negative real numbers. Then, f is :

MCQ (Single)One-to-One (Injective) FunctionOnto (Surjective) FunctionBijective Function

Let A = R – {5} and B = R – {1}. Consider the function f : A → B, defined by f(x) = (x – 3)/(x – 5). Show that f is one-one and onto.

A function f : ℝ → ℝ defined as f(x) = x² - 4x + 5 is :

A function f : A → B defined as f(x) = 2x is both one-one and onto. If A = {1, 2, 3, 4}, then find the set B.

Evaluate : sin⁻¹(sin 3π/4) + cos⁻¹(cos 3π/4) + tan⁻¹(1)