Question 1178867
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Interchanging x and y in a given function and solving for the new y is a good formal mathematical method for finding inverses; but it is overkill for a simple example like this.<br>
An informal way to find the inverse of many relatively simple functions is to think in terms of an inverse "undoing" what the function does.  That is, two functions are inverses of each other if, when you take an input and operate on it with one function and then the other, you get back to the original input.<br>
That informal way of thinking makes this problem easy.<br>
The function F(x) says "multiply the input by 9".
The function G(x) says "divide the input by 9".
The function H(x) says "divide 9 by the input".<br>
Which two of those functions "undo" each other?  Stated differently, for which two of those functions is it true that taking an input, applying one function and then the other, gets you back to the original input?<br>
Clearly the answer is "multiply by 9 and then divide by 9" (or "divide by 9 and then multiply by 9").<br>
ANSWER: F(x) and G(x) are inverses of each other.<br>