You can put this solution on YOUR website! The standard way I have seen taught for finding an inverse function is to switch the x and y variables and solve for the new y.
That makes sense, because an inverse function is supposed to "un-do" what the function does.
So let's do this.
-->
Now solve the new equation for y.
Now here is a faster way to reach the same answer without the formal algebra. It will work for many relatively simple functions.
Again, think about the fact that the inverse function is supposed to "un-do" what the function does.
So look at the original function. What does it "do" to x to get y? It does these three things, in order:
(1) multiply by 5
(2) add 4
(3) divide by 7
To "un-do" what the function does, the inverse function should do the opposite operations, in the reverse order:
(1) multiply by 7 ( --> )
(2) subtract 4 ( --> )
(3) divide by 5 ( --> )
You can see that we get the same answer as with the formal algebra; not only that, but the steps are EXACTLY THE SAME as with the formal algebraic method.
You might want to try this method the next time you need to find an inverse function, to see if the method "works" for you.
