The function f is called constant function, if every element of A has the same image in B.
Range of a constant function is a singleton set.
Let A = {x, y, u, v, 1 }, B = {3, 5, 7, 8, 10, 15}.
The function f : A ---> B defined by f (x) = 5 for every x belonging to A is a constant function.
The figure given below represents a constant function.
Problem 1 :
Let f : X ----> Y. X, Y and f are defined as
X = {a, b, c, d}
Y = {d, e, f}
f = {(a, e), (b, e), (c, e)}
Is f constant function ? Explain.
Solution :
Write the elements of f (ordered pairs) using arrow diagram as shown below.
In the above arrow diagram, every element of X has the image "e" in Y.
So, f is a constant function.
Problem 2 :
Let f : A ----> B. A, B and f are defined as
A = {1, 2, 3, 4}
B = {5, 6, 7, 8}
f = {(1, 8), (2, 6), (3, 5), (4, 7)}
Verify whether f is a function. if so, what type of function is f ?
In the above arrow diagram, every element of A does not have the same image in B.
So, f is not a constant function.
One to one or Injective function
One to one and Onto or Bijective function
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