1. Tardigrade
  2. Question
  3. Mathematics
  4. Let X be the set of all positive integer greater than or equal to 8 and let f: X arrow X be a function such that f(x+y)=f(x y) for all x ≥ 4, y ≥ 4. If f(8)=9, Determine f(9)

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Q. Let $X$ be the set of all positive integer greater than or equal to 8 and let $f : X \rightarrow X$ be a function such that $f(x+y)=f(x y)$ for all $x \geq 4, y \geq 4$. If $f(8)=9$, Determine $f(9)$

Relations and Functions - Part 2

Solution:

We observe that
$f (9) = f(4 + 5) = f(4 · 5) = f(20) = f(16 + 4)$
$= f(16 · 4) = f(64) = f(8 · 8)$
$= f(8 + 8) = f(16) = f(4 · 4) = f(4 + 4) = f(8) = 9$