SOLUTION: If f(x)=square root of x-1 find f-1(x)

Question 112746: If f(x)=square root of x-1 find f-1(x)
Found 2 solutions by mathnard, solver91311:
Answer by mathnard(10) (Show Source): You can put this solution on YOUR website!
This is an inverse functions problem. f(x) is read f of x, not f times x and is just a fancy way of saying y. so really what they are saying is:

To find an inverse, which is what means, you switch the x and y and then solve for the new y:

square both sides:

so

add 1 to both sides

This means that the inverse function is:

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
I think you mean: If , then find .

The first thing you have to do is determine whether exists. There is a pretty simple test that will tell you. It is called the horizontal line test.

Step 1: Graph the original function.

Step 2: If ANY possible horizontal line intersects the graph in more than one place, then we know that is NOT a function, i.e. f does NOT have an inverse. Otherwise, does exist and f does have an inverse. For this example, there is no horizontal line that intersects the graph more than once, so we know that f has an inverse. Now, and only now, can we set about finding it.

Procedure to find the inverse of a one-to-one function (one that has an inverse):

Step 1: Replace f(x) with y.

Step 2: Swap the positions of the x and y variables with each other.

Step 3: Rearrange the equation so that it again is showing y as a function of x, i.e. solve for y.

Ok, Super-Double-Plus Extra Credit. If , does exist?

Hope this helps
John
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