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 :

Show that a function f : R → R defined by f(x) = 2x/(1 + x²) is neither one-one nor onto. Further, find set A so that the given function f : R → A becomes an onto function.

A relation R is defined on N × N (where N is the set of natural numbers) as : (a, b) R (c, d) ⇔ a – c = b – d. Show that R is an equivalence relation.