Let f be the set of all integers greater than or equal to 8 and f :

1.	Let f be the set of all integers greater than or equal to 8 and f : X → X be a function such that f(x + y) = f(xy) for all x ≥ 4, y ≥ 4. if f(8) = 9, determine f(9).
Answer» Explanation: We observe that f(4 + 5) = f(4.5) = f(20) = f(16 + 4) = f(16.4) = (64) = f(8.8) = f(8 + 8) = f(16) = f(4 + 4) = f(8). If f(8) = 9, then f(9 = 9) This is one string. There may be other different way changing f(8) from f(9). The important thing to be observed is the fact that the f(x + y) = f(xy) applies only when x and y are at least 4. One may string using x and y which are smaller then 4, but that is not valid. For example f(9) = f(3.3) = f(3 + 3) = f(6) = f(4 + 2) = f(4.2) = f(8), (is filled string.)

Let f be the set of all integers greater than or equal to 8 and f : X → X be a function such that f(x + y) = f(xy) for all x ≥ 4, y ≥ 4. if f(8) = 9, determine f(9).

Answer»

Explanation:

We observe that

f(4 + 5) = f(4.5) = f(20) = f(16 + 4) = f(16.4) = (64) = f(8.8)

= f(8 + 8) = f(16) = f(4 + 4) = f(8).

If f(8) = 9, then f(9 = 9) This is one string. There may be other different way changing f(8) from f(9). The important thing to be observed is the fact that the f(x + y) = f(xy) applies only when x and y are at least 4. One may string using x and y which are smaller then 4, but that is not valid. For example

f(9) = f(3.3) = f(3 + 3) = f(6) = f(4 + 2) = f(4.2) = f(8), (is filled string.)

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