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Operations on Functions

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Calculus and Analytical Geometry
MTH101
LECTUER ­ 7
Operations on Functions
Example:
Then their sum is defined by
Now we compare the domains of original
functions f and g, and their sum:
Let us take two functions
sum of these functions are
Example: Now consider the two functions
Then their product is defined by
Note that
Now we compare the domains of original
functions f and g, and their product:
Mth101
Page 19
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Calculus and Analytical Geometry
Operations on Functions
Some time we write the product of two same
Consider the function
functions as
In general, if n is positive integer, then
For example,
Remark : Note that we can express the function as
Let us suppose two functions
Now if we substitute g(x) for x in the formula
for f we obtain a new function denoted by
Also we can write
Note that in general we cannot write
Example: Here
Then composition of these functions are
Now we compare the domains of original
functions f and g, and their composition
Mth101
Page 20