SOLUTION: Find f^-1 for f(x)= √x -3

Question 1165152: Find f^-1 for f(x)= √x -3
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

Don't use the "√" symbol in your posts. We don't know whether "√x -3" is supposed to be or .

The standard algebraic method for finding the inverse of a function (which you should know!) is to switch the x and y and solve for the new y.

I will instead show a quick and easy way to find the inverse of simple functions like this, based on the concept that an inverse function "gets you back where you started".

(1) Supposing the given function is , the operations performed on the input are (a) take the square root and (b) subtract 3.

The inverse function, to get you back where you started, has to (a) add 3 and (b) square the result.

So the inverse function in this case is .

(2) If the function is , then the operations performed are (a) subtract 3 and (b) take the square root.

So the inverse function, in that case, has to (a) square the input and (b) add 3.

So the inverse function in that case is

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