Thread: When A Function Is to the power of -1

When A Function Is to the power of -1what does it mean?

Originally Posted by abc10

When A Function Is to the power of -1what does it mean?

It can have two meanings.

If you take the literal meaning for "power of -1", then

.


But the more-often used meaning for this notation is the "Inverse Function"

Basically, if you have a function , then the inverse function is the function whose graph is a reflection along the line . So the and values have swapped. Also, the domain and range have also swapped.

Expanding slightly on what prove it said.

A function to the power one -1 is the inverse of that function.

the inverse of a number is a number that multiplied by the original equals 1.
always.


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Hello abc10

Just to expand a little further on the replies so far:

Yes, denotes the inverse of the function .

Let's take a simple function like . Then, for example:

... and so on.

Then is the function that reverses this process. So:

... and so on.

Perhaps you can work out what does? Since multiplies by and then adds , will do the 'opposite' things in the reverse order. In other words, will:

• subtract ; and then
  

• divide by .

So:

(Try this function with the values , and and check that you get , and .)

Grandad