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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 )
Given f ( x ) = x 2 - 2 x + 8 and g( x ) = √(x+ 6) evaluate f (3) and g(3) Solution Okay we've two function evaluations to do here and we've also obtained two functions
The following is a double inequality. -9 In a double inequality we are saying that both of the inequalities
y-5=2x
$73.62 0.06
Let's begin with the graph of couple of polynomials. Do not worry regarding the equations for these polynomials. We are giving these just so we can utilize them to show so
10x-25y+5=0
3y-4=14
Perpendicular to y=3x-2 and through the point (6,4)
What is ALgebra
The difference of two numbers is 18. The larger number is four more than twice the smaller. What are the numbers?
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