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let f(x)=sqrt(1+x^2) then...

let `f(x)=sqrt(1+x^2)` then

A

` f(xy)=f(x)*f(y)`

B

`f(xy)gef(x)*f(y)`

C

`f(xy)lef(x)*f(y)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have, `f(x)=sqrt(1+x^(2))`
`f(xy)=sqrt(1+x^(2)y^(2))`
`f(x)*f(y)=sqrt(1+x^(2))*sqrt(1+y^(2))`
`=sqrt((1+x^(2))(1+y^(2)))`
`sqrt(1+x^(2)+y^(2)+x^(2)+y^(2))`
`:. sqrt(1+x^(2)y^(2))lesqrt(1+x^(2)+y^(2)+x^(2)+y^(2))`
`rArr f(xy)lef(x)*f(y)`
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