Inverse functions, Algebra

Assignment Help:

In 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 these are very special functions. Let's see what makes them so special.  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 first one we plugged x = -1 into 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 that we begin with.

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

Note that here we actually are doing some function composition.

The first one is actually,

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

and the second one is,

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

So, just what is going on here?  In some manner we can think of these two functions as undoing what the other did to number.  In the first one 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. Before formally explaining inverse functions and the notation which we're going to employ for them we have to get a definition out of the way.


Related Discussions:- Inverse functions

Linear equations, one no. is 7 more than another and its square is 77 more ...

one no. is 7 more than another and its square is 77 more than the square of the smaller number.What are the numbers?

Horizontal asymptote, Also, as x obtain very large, both positive & negativ...

Also, as x obtain very large, both positive & negative, the graph approaches the line specified by y = 0 .   This line is called a horizontal asymptote. Following are the genera

Standard form, 4(x)^2-40x+107 in standard form

4(x)^2-40x+107 in standard form

#title.MAt 104., #questionProvide one example to show how you can use the E...

#questionProvide one example to show how you can use the Expected Value computation to assess the fairness of a situation (probability experiment). Provide the detailed steps and c

Exponential functions, Definition of an exponential function If b is an...

Definition of an exponential function If b is any number like that b = 0 and b ≠ 1 then an exponential function is function in the form,

Solving system graphically, #questionSolve the system graphically. If the s...

#questionSolve the system graphically. If the system has an infinite number of solutions, use set builder notation to write the solution set. If the system has no solution, state t

Problems with fractions , The sum of the sides of a triangle is 9 2/9 inche...

The sum of the sides of a triangle is 9 2/9 inches.If the two sides measure 5/3 inches and 3 1/6 inches,find the measure of the third side

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd