Let f : W → W be defined as show that f is invertible. Find the inverse of f,where W is the set of all whole numbers.
Let R be a relation defined on the set of natural numbers N as follow :
R = {(x, y) : and 2x + y = 24}
Find the domain and range of the relation R. Also,find if R is an equivalence relation or not.
Let f : N → R be a function defined as f(x) = 4x² + 12x + 15. Then show that f : N → S, where S is range of f, is invertible. Also find the inverse of f.
How many equivalence relations on the set {1, 2, 3} containing (1, 2) and (2, 1) are there in all ?Justify your answer.
Consider given by f(x) = 5x² + 6x – 9.Prove that f is invertible with f⁻¹(y) = [where, R⁺ is the set of all nonnegative real numbers.]
Find the equations of the normal to the curve x² = 4y which passes through the point (1, 2).
Show that the relation S in the set R of real numbers defined as S = {(a, b) : a, b ∈ R and a ≤ b³} is neither reflexive nor symmetric nor transitive.
For the curve y = 4x³ – 2x⁵, find all those points at which the tangent passes through the origin.
If C = 0·003x³ + 0·02x² + 6x + 250 gives the amount of carbon pollution in air in an area on the entry of x number of vehicles, then find the marginal carbon pollution in the air, when 3 vehicles have entered in the area.