SOLUTION: let f(x)=2x-3 find each value (fof-1)(5)

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Question 1094700: let f(x)=2x-3
find each value
(fof-1)(5)
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

I'm sure what you mean is f^-1(5), or "f inverse of 5".

When you are asked to evaluate a function for a given input value, what you need to do is use the given function to determine what output value is produced by the given input value. Algebraically, you simply plug the given input value into the function and evaluate.

When you are asked to find "f inverse of 5", you are "going the other way". That is, you are given the output value, and you are being asked to find what input value of x in the given function produces that given output value. Algebraically, you set the output value (the function value) to the given output (y) value, and you solve the resulting equation to find the required input (x) value.





The required input value, to get an output value of 5, is 4.

or...

"f inverse of 5 is 4"
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
let f(x)=2x-3
find each value
(fof-1)(5)
~~~~~~~~~~~~~~~~~

So, the question (after editing) is 

    "find the value ".


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 =  =  = 4.


Thus    = 4.


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


Answer.  (fof^(-1))(5) = 5.

     Or   = 5.


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.



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