Question 1094700
.
let f(x)=2x-3 
find each value 
(fof-1)(5)
~~~~~~~~~~~~~~~~~


So, the question (after editing) is 


<pre>
    "find the value {{{(fof^(-1))(5)}}}".
</pre>

<pre>
First,  we must calculate  f^(-1)(5).


f^(-1)  of  5  is  that  "x"  which  makes  2x-3  equal to  5:  2x-3 = 5.


It is easy to see  (by solving this equation)  that  x = {{{(5+3)/2}}} = {{{8/2}}} = 4.


Thus   {{{f^(-1)(5)}}} = 4.


Next,  we must calculate f(4).  It is more than easy:  f(4) = 2*4 - 3 = 8-3 = 5.


<U>Answer</U>.  (fof^(-1))(5) = 5.

     Or  {{{(fof^(-1))(5)}}} = 5.
</pre>


Notice that we started with the number 5, and ended with the same number.


This fact is not a random event.


Until the functions f and f^(-1) are one-to-one onto-maps, the composition (fof(-1)) is identical map.



If the meaning of these words goes out of your understanding now, then, perhaps, you will learn it later in your further studying of Math.