Types of Functions

Show that the function f : N → N defined by f(x) = 2x – 1 is one-one but not onto

Show that the function f : N → N defined by f(m) = m² + m + 3 is one-one function

In the following case state whether the function is bijective or not. Justify your answer

f: R → R defined by f(x) = 2x + 1

In the following case state whether the function is bijective or not. Justify your answer

f: R → R defined by f(x) = 3 – 4x²

Let A = {–1, 1} and B = {0, 2}. If the function f: A → B defined by f(x) = ax + b is an onto function? Find a and b

The distance S object travel under the influence of gravity in time t seconds is given by S(t) = `1/2` gt² + at + b where, (g is the acceleration due to gravity), a, b are constant. Verify whether the function S(t) is one-one or not.

Multiple choice question :

Let A = {1, 2, 3, 4} and B = {4, 8, 9, 10}. A function f: A → B given by f = {(1, 4), (2, 8), (3, 9), (4, 10)} is a

Multiple choice question : 

If f : A → B is a bijective function and if n(B) = 7, then n(A) is equal to