is the inverse function of f(x) written f ⁻¹(x)....or f ⁻¹(y)?

[Phavonic]

is the inverse function of f(x) written f ⁻¹(x)....or f ⁻¹(y)?

I have a maths test book that asks me the inverse, for instance, of


f:x --> 1 - x


And gives the answer as


f ⁻¹:y --> 1 - y


This seems a bit different from what I had learned on the net. I was sure that the inverse of f(x) is f ⁻¹(x), but the above makes me think it could be f ⁻¹(y)


The changing the subject of a formula is the easy part, it's just the usage of x and y that has seemed ambivalent to me. Thanks.

 

[Phavonic]

I have a maths test book that asks me the inverse, for instance, of


f:x --> 1 - x


And gives the answer as


f ⁻¹:y --> 1 - y


This seems a bit different from what I had learned on the net. I was sure that the inverse of f(x) is f ⁻¹(x), but the above makes me think it could be f ⁻¹(y)


The changing the subject of a formula is the easy part, it's just the usage of x and y that has seemed ambivalent to me. Thanks.

PS I don't know why the angry face appeared, it should read f:x--> 1 - x

 

[Phavonic]

PS I don't know why the angry face appeared, it should read f:x--> 1 - x

well...... colon x

So annoying!

 

[Dr.Peterson]

I have a maths test book that asks me the inverse, for instance, of

f: x --> 1 - x

And gives the answer as

f ⁻¹: y --> 1 - y

This seems a bit different from what I had learned on the net. I was sure that the inverse of f(x) is f ⁻¹(x), but the above makes me think it could be f ⁻¹(y)

The changing the subject of a formula is the easy part, it's just the usage of x and y that has seemed ambivalent to me. Thanks.

The variable in a function is arbitrary, sometimes called a dummy variable. It doesn't matter whether you say f^-1(x) = 1 - x or f^-1(y) = 1 - y; they mean exactly the same thing.

In some contexts, it makes more sense to retain the original names for the variables, and in other contexts it makes more sense to always use x. As a result, textbooks vary in which way they do it.

Here is a discussion of this idea: Inverting, Subverted. For more, see To Invert Functions, First Subvert Routine.

(To avoid the appearance of anger, put a space after your colon, as I did above.)

 

[Phavonic]

The variable in a function is arbitrary, sometimes called a dummy variable. It doesn't matter whether you say f^-1(x) = 1 - x or f^-1(y) = 1 - y; they mean exactly the same thing.

In some contexts, it makes more sense to retain the original names for the variables, and in other contexts it makes more sense to always use x. As a result, textbooks vary in which way they do it.

Here is a discussion of this idea: Inverting, Subverted. For more, see To Invert Functions, First Subvert Routine.

(To avoid the appearance of anger, put a space after your colon, as I did above.)

OK, thank you.

So if the test asks me what is the inverse function of f: x ---> 2x + 4 I can answer either

f^-1(x) = (x - 4)/2

f^-1(y) = (y - 4)/2

Is that right?

 

[Dr.Peterson]

OK, thank you.

So if the test asks me what is the inverse function of f: x ---> 2x + 4 I can answer either

f^-1(x) = (x - 4)/2

f^-1(y) = (y - 4)/2

Is that right?

Yes. Or f^-1(t) = (t - 4)/2, or whatever.