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Here are two one-to-one functions f (x ) and g ( x ) if
(f o g )( x ) = x AND ( g o f ) ( x ) = x
then we say that f ( x )& g ( x ) are inverses of each other. More particularly we will say that g ( x ) is the inverse of f ( x ) and specified it by
g ( x ) = f -1 ( x )
Similarly we could also say that f ( x ) is the inverse of g ( x )and specified it by
f (x ) = g -1 ( x )
The notation which we use really based upon the problem. In most of the cases either is acceptable.
For the two functions which we started off this section along with we could write either of the following two sets of notation.
f ( x ) = 3x - 2 f -1(x) = x /3+ 2/3
g ( x ) = x/3 + 2/3 g -1 (x ) = 3x - 2
Now, be careful along with the notation for inverses. The "-1" is not an exponent in spite of the fact that is certain does look like one! While dealing with inverse functions we've got to keep in mind that
f-1(x) ≠ 1/ f ( x )
Now we need to discuss the new method of combining functions. The new way of combining functions is called function composition. Following is the definition. Given two functions
Alex lives .4 miles from the park, beth lives .8 miles from the park. To run equal distances Alex runs 8 times around the park and Beth run 6 times around the part. Write an equati
-6k+7k
37/K^2-K-30
We'll begin this section by defining just what a root or zero of a polynomial is. We say that x = r is a root or zero of a polynomial, P ( x) , if P ( r )= 0 . In other terms x=
four hundred, sixteen million,forty-five
__5n^2)_______ multiplied __(3)____ (3n^2) (n)
How to find the hcf of 36a and 12ab
4 more than a number is 12
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