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Let f be a function defined from R^(+)ra...

Let f be a function defined from `R^(+)rarrR^(+).` If `(f(xy))^(2)=x(f(y))^(2)` for all positive numbers x and y, If `f(2)=6,` find `f(50)`=?

A

20

B

30

C

5

D

40

Text Solution

Verified by Experts

The correct Answer is:
B
`(f(xy))^(2)=x(f(y))^(2) and f(2)=6`
Put x = 25 and y = 2
`(f(50))^(2)=25(f(2))^(2)=25xx36`
`therefore" "f(50)=30`
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