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If f and g are inverse functions, f (6) = 5 and f (2) = 6, find g (6).

If f and g are inverse functions, f (6) = 5 and f (2) = 6, find g (6). solve
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3 Answers

The whole idea of an inverse function is that whatever one function does, the inverse undoes it.
 
So f(6)=5 means when f acts on 6, the result is 5....so the inverse would take 5 back to 6...or g(5)=6
So f(2)=6 means that f reassigns 2 to 6....so the inverse would take 6 back to 2....or g(6)=2
 
So g(6) comes out to be 2.
 
Hope this helped.
f(6) = 5 is information unrelated to the question.
 
f(2) = 6      then
g(6) = 2
Although it is certainly “fair game” to ask such a question to determine whether you understand the concept, I always feel silly when I find out the answer – sort of like a little kid’s joke.

The concept of function is important – there is, at most, one y for each x.

An inverse function is also a function, but it goes the other way:  there is., at most, one x for each y.

O.K., since g is the inverse function of f and f(2) = 6 then g(6)=2.        (this seems silly to me)

Now, just to confuse us, the question writer gave TMI (too much information) with the part that says F(6)=5.  That has nothing to do with our solution (unless you don’t understand the problem).

Comments

So sorry that you feel "silly" about this exercise. Perhaps the cause is a conflation of the notation of "x" and "y" and the concept of input and output (just like computer programming).
 
A function and it's inverse function are similar to sitting down and standing up. One "undoes" the other.
If the function "f" takes an input of 2 and gets an output of 6, then the inverse function "g" takes the input 6 and produces the output 2. 
 
 
To Mark M.,  Thanks for you concern.  I wanted to relate to a student who is about to realize how super-simple this concept is;  the light bulb goes on (and you feel like the teacher is not teaching, but tricking you -- like a little kid's joke).
 
My oldest memory of such an incident was sixth grade and I stood to define a word on the vocabulary list on the board.  I pronounced fatigue as FAT-E-GU and the class erupted in laughter.
 
True story:  A Marketing Executive was presenting PowerPoint slides about his company's software expertise and read the bullet as "Our Company is Experienced at Fours and Fives," but the bullet showed IV&V (Independent Verification & Validation).  The commanding general wasn't impressed.