#### Question

Which of the following functions from *A* to *B* are one-one and onto?

*f*_{1} = {(1, 3), (2, 5), (3, 7)} ; *A* = {1, 2, 3}, *B* = {3, 5, 7}

#### Solution

*f*_{1} = {(1, 3), (2, 5), (3, 7)} ; *A* = {1, 2, 3}, *B* = {3, 5, 7}

**njectivity:***f*_{1} (1) = 3*f*_{1}_{ }(2) = 5*f*_{1} (3) = 7

⇒ Every element of *A *has different images in *B*.

So, *f*_{1} is one-one.

Surjectivity:

Co-domain of *f*_{1} = {3, 5, 7}

Range of *f*_{1} =set of images = {3, 5, 7}

⇒ Co-domain = range

So, *f*_{1} is onto.

Is there an error in this question or solution?

Solution Which of the Following Functions From A To B Are One-one and Onto? F1 = {(1, 3), (2, 5), (3, 7)} ; A = {1, 2, 3}, B = {3, 5, 7} Concept: Types of Functions.