# INTO FUNCTION

Let f : A ----> B be a function.

There exists even a single element in B having no pre-image in A, then f is said to be an into function.

The figure given below represents a one-one function. ## Solved Problems

Problem 1 :

Let f : A ----> B. A, B and f are defined as

A  =  {1, 2, 3}

B  =  {5, 6, 7, 8}

f  =  {(1, 5), (2, 8), (3, 6)}

Is f into function? Explain.

Solution :

Write the elements of f (ordered pairs) using arrow diagram as shown below In the above arrow diagram, all the elements of A have images in B and every element of A has a unique image.

That is, no element of A has more than one image.

So, f is a function.

There exists an element 7 in B having no pre-image in A.

Therefore, f is into function.

Problem 2 :

Let f : X ----> Y. X, Y and f are defined as

X  =  {a, b, c, d}

Y  =  {d, e, f}

f  =  {(a, e), (b, f), (c, e), (d, d)}

Is f into function ? Explain. In the above arrow diagram, all the elements of X have images in Y and every element of X has a unique image.

That is, no element of X has more than one image.

So, f is a function.

Every element of Y has a pre-image in X.

So, f is not into function.

## Related Topics

One to one or Injective function

Onto or Surjective function

One to one and Onto or Bijective function

Constant Function

Identity function Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

## Recent Articles May 26, 23 12:27 PM

Adaptive Learning Platforms: Personalized Mathematics Instruction with Technology

2. ### Simplifying Expressions with Rational Exponents Worksheet

May 21, 23 07:40 PM

Simplifying Expressions with Rational Exponents Worksheet