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)

Question

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) (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

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

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

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

Q. Let X be the set of all positive integer greater than or equal to 8 and let 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)

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

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

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