PUMPA - SMART LEARNING
எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்
Book Free DemoAmong the numerous functions available, there are a few unique cases of functions.
Let us look at a few of the special cases of functions.
1. Constant functions
2. Identity functions
3. Real valued function
Let us now look at each of them in detail.
1. Constant functions
A function A \rightarrow B is said to be a constant function if all the elements in A have the same image in B.
Example:
In the example given above, all the preimages x_1, x_2, x_3, x_4 and x_5 have the same image 16.
The given constant function can also be represented as f(x) = 16.
2. Identity function
A function A \rightarrow B is said to be an identity function if the elements of A are equal to its image in B.
That is, \text{Elements in }A = \text{Image in }B.
Example:
Let us look at the example given below for a better understanding.
Consider the image given above.
\text{Preimage in }A = x_1
\text{Its image in }B = x_1
Therefore, for every element in A, there is an equal image in B.
Also, the given arrow diagram can be represented as f(x) = x.
3. Real valued function
A function f : A \rightarrow B is said to be a real-valued function if all the elements in the range belong to the set of real numbers, R.
That is, f(A) \subseteq R.
Example:
Some of the few examples of real-valued functions are:
1. f(x) = 3x - 8
2. f(x) = x^3
3. f(x) = \frac{2}{x}
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