If A = (1, 2, 3}, B = {6, 7, 8} is a function such that f(x) = x + 5 then what type of a function is f?

The correct option/answer is "one-one onto".

To understand why this is the correct answer, let us analyze the function step-by-step.
We are given two sets:
Set A={1,2,3} (which is the domain of the function)
Set B={6,7,8} (which is the co-domain of the function)

The function is defined as:
f(x)=x+5

Step 1: Find the images of the elements of set A under function f
Let us calculate the value of f(x) for each element x in the domain A:
For x=1:
f(1)=1+5=6
For x=2:
f(2)=2+5=7
For x=3:
f(3)=3+5=8

Thus, the set of images (Range of the function) is:
Range ={6,7,8}

Step 2: Check if the function is One-One (Injective)
A function is one-one if distinct elements in the domain have distinct images in the co-domain.
Here, we observe:
- The element 1 maps uniquely to 6.
- The element 2 maps uniquely to 7.
- The element 3 maps uniquely to 8.
Since no two different elements in set A have the same image in set B, the function f is one-one.

Step 3: Check if the function is Onto (Surjective)
A function is onto if every element in the co-domain (set B) has a corresponding pre-image in the domain (set A). In other words, the Range must equal the Co-domain.
Here, the Co-domain is B={6,7,8} and the computed Range is {6,7,8}.
Since Range = Co-domain, every element in set B is mapped to. Therefore, the function f is onto.

Conclusion
Since the function f is both one-one and onto, it is classified as a one-one onto (bijective) function.