## Inverse functions, Mathematics

Assignment Help:

Inverse Functions : In the last instance from the previous section we looked at the two functions

f ( x ) = 3x - 2 and g ( x ) = x /3+ 2/3 and saw that

( f o g ) ( x ) = ( g o f ) ( x ) = x

and as noted in that section it means that there is a nice relationship among these two functions.  Let's see what that relationship is.  Assume the following evaluations.

f ( -1) = 3( -1) - 2 = -5

⇒         g ( -5) = -5 /3+ 2/3 = -3/3 = -1

g ( 2) = 2/3 + 2/3 =4/3

⇒         f ( 4 /3) = 3( 4/3 ) - 2 = 4 - 2 = 2

In the first case we plugged x = -1 in f (x) and got a value of -5.  Then we turned around and plugged x = -5 into g (x) and got a value of -1, the number which we started off with.

In the second case we did something same.  Here we plugged x = 2 into g ( x ) and got a value of 4/3, we turned around & plugged this into f ( x ) and got a value of 2, that is again the number that we begun with.

Note that we actually are doing some function composition here. The first case is,

( g o f ) ( -1) = g [f ( -1)]= g (-5) =-1

and the second case is,

( f o g ) ( 2) = f [g ( 2)] =f(4/3)=2

Note that these both agree with the formula for the compositions which we found in the previous section.  We get back of function evaluation the number which we originally plugged into the composition.

Thus, just what is going on here?  In some of the way we can think of these two functions as undoing what the other did with number.  In the primary case we plugged x = -1 into f ( x ) and then plugged the result from this function evaluation back into g (x ) and in some way g (x ) undid what f ( x ) had done to x = -1 and gave us back the original x which we started with.

Function pairs which exhibit this behavior are called inverse functions. Previous to formally defining inverse functions & the notation which we're going to use for them we have to get a definition out of the way.

#### Simplified radical form, If we "break up" the root into the total of two pi...

If we "break up" the root into the total of two pieces clearly we get different answers. Simplified radical form: We will simplify radicals shortly so we have to next

#### Numeros complejos, como realizar la i elevavda a la 243

como realizar la i elevavda a la 243

#### Profit and loss ., A story based on profit and loss

A story based on profit and loss

#### Example of mathematical operations, Example of mathematical operations: ...

Example of mathematical operations: Example: Solve the following equation: [2 .( 3 + 5) - 5 + 2] x 3 =  ________   Solution: a.         Perform operations with

#### Find the largest clique, Generate G(1000,1/2) and find the largest clique ...

Generate G(1000,1/2) and find the largest clique you can.  A clique is a complete sub graph, that is, a set of vertices each pair of which is connected by an edge.

#### Asymtotes, vwertical and horizontal

vwertical and horizontal

#### Fractions, how to add a fraction with an uncommon denomoninator

how to add a fraction with an uncommon denomoninator

Quadric Surfaces Earlier we have looked at lines and planes in three dimensions (or R 3 ) and when these are used fairly heavily at times in a Calculus class there are several

#### Rhjuu, Ask questutfjion #Minimum 100 words accepted#

Ask questutfjion #Minimum 100 words accepted#

#### Elliptic paraboloid - three dimensional spaces, Elliptic Paraboloid Th...

Elliptic Paraboloid The equation which is given here is the equation of an elliptic paraboloid. x 2 /a 2 + y 2 /b 2 = z/c Like with cylinders this has a cross section  