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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. fofB. gogC. `(f)/(g)`D. gof |
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Answer» 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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