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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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Ira S. | Bilingual math tutor and much moreBilingual math tutor and much more
5.0 5.0 (260 lesson ratings) (260)
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 the inverse would take 5 back to 6...or g(5)=6
So f(2)=6 means that f reassigns 2 to the inverse would take 6 back to 2....or g(6)=2
So g(6) comes out to be 2.
Hope this helped.
Mark M. | Mathematics Teacher - NCLB Highly QualifiedMathematics Teacher - NCLB Highly Qualif...
4.9 4.9 (188 lesson ratings) (188)
f(6) = 5 is information unrelated to the question.
f(2) = 6      then
g(6) = 2
David W. | Experienced ProfExperienced Prof
4.4 4.4 (47 lesson ratings) (47)
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).


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.