Let f: A `rarr` B be one-to-one function such that range of f is (b). Determine the number of elements in A.

Let f : A rarr B and g : B rarr C be onto functions, show that gof is an onto function.

if f(g(x)) is one-one function, then

Let A={1,2,3,4,5} and f:A rarr A be an into function such that f(x) nex forall x in A . Then number of such functions f is:

Let f : X rarr Y be an invertible function. Show that the inverse of f^–1 is f, i.e. (f^–1)^–1 = f

Statement I The equation (x^(3))/(4) - sin pi x + (2)/(3) = 0 has atleast one solution in [-2, 2]. Statement II Let f : [a, b] rarr R be a function and c be a number such that f(a) lt c lt f(b) , then there is atleast one number n in (a, b) such that f(n) = c.

Let f : N rarr N be a function deifned by f(x) = 9x^2 + 6x - 5 . Show that f : N rarr S , where S is the range of 'f', is invertible. Find the inverse of 'f' and hence, find f^-1(43) and f^-1(163)

Let f: R rarr R and g: R rarr R be two given functions such that f is injective and g is surjective. Then which of the following is injective? a. gof b. fog c. gog d. none of these

Let L denotes the number of subjective functions f : A -> B , where set A contains 4 elementset B contains 3 elements. M denotes number of elements in the range of the function f(x) = sec^-1(sgmx) + cosec^-1(sgn x) where sg n x denotes signum function of x. And N denotes coefficient of t^5 in (1+t^2)^5(1+t^3)^8 . The value of (LM+N) is lambda , then the value of lambda/19 is

Let A be the set of all 50 students of class XII in a school. Let f: A rarr N be the function defined by : f (x) = Roll number of the student x. Prove that 'f' is one-one but not onto.

Let f : R rarr R be the functions defined by f(X) = x^3 + 5 , then f^-1 (x) is