According to the given information,

Suppose that:

f(n) be the largest prime divisior of n it is required to given example to explain whether x < y but f(x) > f(y)

So, take an example and explain.

take x = 5 and y = 16

for x = 5 the largest prime divisor of 5 is 5

so, f(5) = 5

for y = 16 the largest prime divisor of 16 is 2

so, f(16) = 2

therefore,

5<16 but 5>2 that is

xf(y)

therefore, the given statement is possible.

Suppose that:

f(n) be the largest prime divisior of n it is required to given example to explain whether x < y but f(x) > f(y)

So, take an example and explain.

take x = 5 and y = 16

for x = 5 the largest prime divisor of 5 is 5

so, f(5) = 5

for y = 16 the largest prime divisor of 16 is 2

so, f(16) = 2

therefore,

5<16 but 5>2 that is

xf(y)

therefore, the given statement is possible.