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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 )
w^2 + 30w + 81= (-9x^3 + 3x^2 - 15x)/(-3x) (14y = 8y^2 + y^3 + 12)/(6 + y) ac + xc + aw^2 + xw^2 10a^2- 27ab + 5b^2 For the last problem I have to incorporate the following words
3X^8+6X^7-9X^6+6X^5 FACTOR THE EXPRESSION
how do I convert 5^1/2 to a percent
In this section we will discussed about non-linear systems of equations. A non-linear system of equations is a system wherein at least one of the variables contains an exponent ot
x=1-yto the second power
f(x) = x3 - 9x + 3
If you deposited $500 for 4 years at 6% annual interest, compounded semi-annually, how much money would you have saved?
The last set of transformations which we're going to be looking at in this section isn't shifts, but in spite of they are called reflections & there are two of them. Reflection
a carpenter had a 20 ft piece of lumber which he cut into 3 pieces. one piece was 7 1/3 ft long and other was 6 1/2 ft long. how long was the remaining piece?
General problems for homework
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