Functions questions

• Aug 3rd 2010, 05:53 PM
brumby_3
Functions questions
The questions are here: Yfrog Image : yfrog.com/mgmathfuncj sorry it never works when I try to upload an image on mathhelpforum for some reason!

So, for example is h(17) just h(17) = 17/4 = 4.25? But for this, isn't it not defined as it is not within the set said N --> {0, 1, 2, 3}

k(5) = 2 x (5)^2 + 1 = 51

L(6) = 2 x 6 = 12.

Am I on the right track with these kind of questions or completely lost?
• Aug 3rd 2010, 06:52 PM
tonio
Quote:

Originally Posted by brumby_3
The questions are here: Yfrog Image : yfrog.com/mgmathfuncj sorry it never works when I try to upload an image on mathhelpforum for some reason!

So, for example is h(17) just h(17) = 17/4 = 4.25?

No, why? When you divide 17 by 4 the residue is 1, since $\displaystyle 17=4\cdot4+1$ , so h(17)=1...

But for this, isn't it not defined as it is not within the set said N --> {0, 1, 2, 3}

k(5) = 2 x (5)^2 + 1 = 51

L(6) = 2 x 6 = 12.

Am I on the right track with these kind of questions or completely lost?

You're right in the last two functions.

Tonio
• Aug 3rd 2010, 08:22 PM
brumby_3
For g(7), do I do g(7+1) = g(8) = 1+ (g(7)/2)
But then I'm confused lol.

And also could I get some help with f o h(3), I can't figure it out. :(

Thanks!
• Aug 3rd 2010, 11:36 PM
emakarov
Quote:

For g(7), do I do g(7+1) = g(8) = 1+ (g(7)/2)
No, you have to represent the argument 7 as n + 1. I.e., g(7) = g(6 + 1) = 1 + g(6) / 2. At this point it may be easier to forget about g(7) and calculate g(6) first. And for that you have to compute g(5), etc.

By definition, f o h(3) = f(h(3)).
• Aug 4th 2010, 04:36 PM
brumby_3
For f o h (3), my answer is 1, but for h o f(3), is the answer 1 as well or 3?
• Aug 5th 2010, 01:38 AM
emakarov
Quote:

for h o f(3), is the answer 1 as well or 3?
It is also 1: f(3) = 1 and h(1) = 1. Here the answer is the same because h(n) = n for n < 4, and the composition of f with the identity function does not change f, whether the identity function is applied first or last. In general, however, the order of functions in composition matters. For example, h(f(2)) = 0, but f(h(2)) = 4.