Question

A function f is defined from R → R as f(x) = ax + b, such that f(1) = 1 and f(2) = 3. Find function f(x). Hence, check whether function f(x) is one-one and onto or not.

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 :

Assertion (A): The relation R = {(x, y) : (x + y) is a prime number and x, y ∈ N} is not a reflexive relation. Reason (R): The number '2n' is composite for all natural numbers n.

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

Let S be the relation defined by S = {(l₁, l₂) : l₁ is perpendicular to l₂}, check whether the relation S is symmetric and transitive.