Need to create a function in Precalc

[suej173]

Need to create a function in Precalc...

Homework Statement

Let a be the # corresponding to the first letter of your name in the alphabet. Let b be the # corresponding to the first letter of your last name. Come up with a function f such that f(a)=b and f(b)=a (you need to write the answer as y=f(x)).

Homework Equations

My #'s would be f(19)=10 and f(10)=19

The Attempt at a Solution

I would just like some help starting off...I feel a bit lost. Thanks for your time!

 

[skiller]

Hi suej173!

There is obviously the trivial function, but assuming you want more than that, then:

If a and b are given, then as you only have 2 points to work with, the simplest solution would be the function describing a straight line through these 2 points. Does this help?

If you want y to be a function of a and b also (which I'm guessing is what you're after), then f(x,a,b) is a bit more complicated. Hmmm, I'll think about that one.

 

[HunterDX77M]

I agree with oay, a linear equation would be the quickest and simplest way to do this. The two necessary parts to your function are that f(19) = 10 and f(10) = 19. If your equation is in the form f(x) = y, then you can think of f(19) = 10 as (19, 10) on a coordinate plane, where 19 is the x-coordinate and 10 is the y-coordinate. What about the other requirement, f(10) = 19? What would be its corresponding point on the coordinate plane?

If you've got two points whose x and y coordinates you know, can you make a function out of that? Hope that helps.

 

[SammyS]

Homework Statement

Let a be the # corresponding to the first letter of your name in the alphabet. Let b be the # corresponding to the first letter of your last name. Come up with a function f such that f(a)=b and f(b)=a (you need to write the answer as y=f(x)).

Homework Equations

My #'s would be f(19)=10 and f(10)=19

The Attempt at a Solution

I would just like some help starting off...I feel a bit lost. Thanks for your time!

If you need y = f(x) and x = f(y), then you would have x = f(f(x)) so that f is a function which is it's own inverse .

 

[skiller]

If you want y to be a function of a and b also (which I'm guessing is what you're after), then f(x,a,b) is a bit more complicated. Hmmm, I'll think about that one.

D'oh! I can't believe I wrote this! I can only put it down to the fact that it was very late at the time (UK time). Sorry!