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If `f: R->R` is a function satisfying `f(x+y)=f(x y)` for all `x ,y` in ` R` and `f(3/4)=3/4`, then `f(9/(16))` is a.`3/4` b. `9/(16)` c. `(sqrt(3))/2` d. 0

A

`(3)/(4)`

B

`(9)/(16)`

C

`(sqrt3)/(2)`

D

`0`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `f(0)=k.` Then `f(x)=f(x+0)=f(0)=k`
So, f is a constant function. But `f((3)/(4))=(3)/(4)`
`therefore" "f(x)=((3)/(4))" for all x and hence "f((9)/(16))=(3)/(4)`
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