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xerocoool
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Manhattan 5lbs : Functions,Formulas,Sequence Q73)

by xerocoool Sun Sep 07, 2014 1:18 pm

Hi Tommy,

Could you please explain the logic for the following problem

1/2 f(x) = f(1/2 x), which is true for all values of f(x) ?

A) f(x) = 2x+2
B) f(x) = 13x
C) f(x) = x^2
D) f(x) = x-10
E) f(x) = sqrt (x-4)

Thanks
xero
tommywallach
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Re: Manhattan 5lbs : Functions,Formulas,Sequence Q73)

by tommywallach Mon Sep 08, 2014 8:56 pm

Hey Xero,

The only way to solve this question (aside from intuitively seeing which one will always be the same) is to test values for all 5 functions. Try doing that in a response to this thread and see how it solves. I'll step in and help if something goes wrong...

-t
xerocoool
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Re: Manhattan 5lbs : Functions,Formulas,Sequence Q73)

by xerocoool Fri Sep 12, 2014 2:51 am

Hi Tommy,

1) f(x) = 2x + 2

1/2 f(x) : 1/2 (2x+2) = x+1
f(1/2 x) : 2(1/2)x + 2 = x+2

Not equal

2) f(x) = 13x
1/2 f(x) = 1/2 (13x) = 13x/2
f(1/2 x) = 13(x/2) = 13x/2

Equal

3) f(x) = x^2
1/2 f(x) = 1/2 (x^2) = x^2/2
f(1/2 x) = [(1/2)x]^2 = x^2/4

Not equal

4) f(x) = x-10
1/2 f(x) = (x-10)/2
f(1/2 x) = (x/2) - 10 = (x-20)/2

Not equal

5) f(x) = sqrt (x-4)
1/2 f(x) = 1/2 sqrt (x-4)
f(1/2x) = sqrt [(x/2)-4] = sqrt [(x-8)/2]

Not equal

Hence "B". For some reason was not able to comprehend the RHS part (i.e. f(1/2x)). Just had to plug in 1/2 x in place of "x" to get the value of f(1/2 x).

Hope the approach is right.

Thanks
xero
tommywallach
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Re: Manhattan 5lbs : Functions,Formulas,Sequence Q73)

by tommywallach Fri Sep 12, 2014 6:04 pm

Hey Xero,

Well done! I realize that my explanation was actually misleading. I said you should try values, but that's exactly what you CANNOT do here. Oy. Apologies.

Your method is indeed the way to do it. You could also have simplified from the beginning like so:

1/2 f(x) = f(1/2x)

-->

f(x) = 2 f(1/2x)

Which might have made things a little bit faster, or even allow you to logic out that only multiplication will render these two things equal.

But either way, you did a great job!

-t
xerocoool
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Re: Manhattan 5lbs : Functions,Formulas,Sequence Q73)

by xerocoool Sat Sep 13, 2014 12:15 pm

Hi Tommy,

Thanks for the feedback.

xero
tommywallach
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Re: Manhattan 5lbs : Functions,Formulas,Sequence Q73)

by tommywallach Tue Sep 16, 2014 3:38 pm

Glad to help!

-t