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Functions

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Source: — Problem Solving |

by vitaly » Fri May 08, 2009 7:51 pm
f(10, 15) = f(25, 14), of course it's the largest. Answer is A.
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by Vemuri » Fri May 08, 2009 11:17 pm
vitaly wrote:f(10, 15) = f(25, 14), of course it's the largest. Answer is A.
The second condition is: f(x,y+1) = f((x,y),y). How did you derive f(25,10)?
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by sureshbala » Fri May 08, 2009 11:58 pm
The answer has to be E and not A.

With some serious observation you can find that f(x, y) = x i.e. that output of the function is independent of y.

We have f(x, 0) = x and f(x, y+1) = f(f(x, y), y)

From the second definition we have,

f(x, 1) = f(f(x, 0), 0) = f(x, 0) = x.

Hence f(x, 1) = x.

F(x, 2) = f(f(x, 1), 1) = f(x, 1) = x

Hence f(x, 2) = x.

So from here you can conclude that f(x, y) = x.

Hence the output of the function with largest value of x will be the largest.

So, the option E.
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by Vemuri » Sat May 09, 2009 1:45 am
sureshbala wrote:The answer has to be E and not A.

With some serious observation you can find that f(x, y) = x i.e. that output of the function is independent of y.

We have f(x, 0) = x and f(x, y+1) = f(f(x, y), y)

From the second definition we have,

f(x, 1) = f(f(x, 0), 0) = f(x, 0) = x.

Hence f(x, 1) = x.

F(x, 2) = f(f(x, 1), 1) = f(x, 1) = x

Hence f(x, 2) = x.

So from here you can conclude that f(x, y) = x.

Hence the output of the function with largest value of x will be the largest.

So, the option E.
Hail Bala Hail !!! That was very smart of you. :)
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