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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 )
Solve each of the following. |x - 2 | = 3x + 1 Solution At first glance the formula we utilized above will do us no good here. It needs the
1/1+x+1/y+1/1+z+1/x+1/1+y+1/z=1
3.4% as a decimal
Polynomial Functions Dividing Polynomials We're going to discussed about dividing polynomials. Let's do a quick instance to remind how long division of polynomials
2x-4=-9
How do you expand a sigma notation from x to x of a variable that is not defined in the index. For example, summation of i=1 to n of x?
SUPPOSE Y IS DIRECTLY PROPORTIONAL TO X AND THAT Y = 35 WHEN X = 5 FIND THE CONSTANT OF PROPORTIONALITY K K=
12 + 5x = 6 - x
(x2/3)-3
5x + 2y = 6 -2x + y = -6
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