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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

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

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