Problem Solving

Let f(x,y) be defined by i. f(x,0)=x and ii. f(x, y+1)= f(f(x,y),y). Which of the following is the largest?

A.f(10, 15)

B. f(11, 14)

C. f(12, 13)

D. f(13, 12)

E. f(14,11)

f(10, 15) = f(25, 14), of course it's the largest. Answer is A.

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)?

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.

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.