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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 )
2x+2=2 then x value?
(-11,-3),(0,-7)
y+7 3y-2 --- = 1 + ---- 3 5
We now can also combine the two shifts we only got done looking at into single problem. If we know the graph of f ( x ) the graph of g ( x ) = f ( x + c ) + k will be the graph of
which of the following cereals is the best buy?
Solve following equations by factoring. a) x 2 - x = 12 b) y 2 + 12 y + 36 = 0 Solution a) x 2 - x = 12 First to solve it get everything on si
Logarithm Functions In this section now we have to move into logarithm functions. It can be a tricky function to graph right away. There is some different notation which you
5x8y+9x=0,y=5
is it free
17b-29=39
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