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Suppose that f is an even function, g is...

Suppose that f is an even function, g is an odd function and both f and g are defined on the entire real line R. Which of the following wherever defined are odd function ?

A

fof

B

gog

C

`(f)/(g)`

D

gof

Text Solution

Verified by Experts

BC
Given, `f(x)=f(-x) and g(x)=-g(-x)`
Let, `F(x)=f[f(x)]impliesF[-x]=f[f(-x)]=f[f(x)]=F(x)implies` F is even.
`G(x)=g[g(x)]implies G(-x)=g[g(-x)]=g(-g(x))=-g(g(x))=-G(x)implies `G is odd
`k(x)=(f(x))/(g(x))impliesk(-x)=(f(-x))/(g(-x))=(f(x))/(-g(x)=-k(x) implies` k is odd
|||1y gof is even.
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