What is the difference between reciprocal and inverse in mathematics?

[singleton]

Er well I've been away from math for a LONG time until I recently began reading into calculus and I have a question.

I always see reciprocal and inverse throughout the text. What is the difference between the two?

I always thought reciprocal was the number (in a fraction form) flipped so the result of any multiplication is always 1.

eg 3/7 is the reciprocal of 7/3

But what about inverse? I'm having a troubling time finding the definitive answer for that. I've been thinking its 1 divided by the number. So the inverse of 47 is 1/47 ?

Tell me how embarassingly wrong I am please :D

 

[Nylex]

Reciprocal means 1/x, but when x is a fraction it does flip. Not really sure how to explain inversing, other than it's kinda "undoing" an operation, eg. if you do x*y and then x*y/y, you get x again cos multiplication and division are inverses. That's probably not very clear :(.

 

[Hurkyl]

You are embarassingly wrong! Okay, now for the serious answer.


The term "inverse" always refers to inverting some sort of operation. The reciprocal is an example of something called a "multiplicative inverse": the inverse of the operation of multiplying by a/b is multiplying by b/a.

One often does not say precisely what is being inverted because it can usually be inferred from the context.

 

[singleton]

Thanks!

I think I have a better idea now what the textbook is talking about when it takes an exponential function and inverts it to get the logarithmic function (I think that is what it is doing at least! rofl)

y = 2^x,

Inverse is x = 2^y. To write it logarithmicly would be y = log2X I think

(sorry I suck at using that tex stuff so the 2 should be a subscript like :)