The total number of functions, f : {1, 2, 3, 4} \(\rightarrow\) {1, 2, 3, 4, 5, 6} such that f(1) + f(2) = f(3), is equal to
- 60
- 90
- 108
- 126
The Correct Option is B
Solution and Explanation
Case 1:If f(3) = 3 then f(1) and f(2) take 1 OR 2
No. of ways = 2⋅6 = 12
Case 2: If f(3) = 5 then f(1) and f(2) take 2 OR 3
OR 1 and 4
No. of ways = 2⋅6⋅2 = 24
Case 3: If f(3) = 2 then f(1) = f(2) = 1
No. of ways = 6
Case 4: If f(3) = 4 then f(1) = f(2) = 2
No. of ways = 6
OR f(1) and f(2) take 1 and 3
No. of ways = 12
Case 5: If f(3) = 6 then f(1) = f(2) = 3 ⇒ 6 ways
OR f(1) and f(2) take 1 and 5 ⇒ 12 ways
OR f(2) and f(1) take 2 and 4 ⇒ 12 ways
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Concepts Used:
Types of Functions
Types of Functions
One to One Function
A function is said to be one to one function when f: A → B is One to One if for each element of A there is a distinct element of B.
Many to One Function
A function which maps two or more elements of A to the same element of set B is said to be many to one function. Two or more elements of A have the same image in B.
Onto Function
If there exists a function for which every element of set B there is (are) pre-image(s) in set A, it is Onto Function.
One – One and Onto Function
A function, f is One – One and Onto or Bijective if the function f is both One to One and Onto function.
Read More: Types of Functions