Find `g o f` and `f o g`, if `f: R rarr R` and `g: R rarr R` are given by `f (x)=cos x` and `g(x)=3 x^2`. Show that `gof` `ne` `f o g`.

Explanation

We have gof .(x)=g(x)=g:(cos x)=3(cos x^2)=3 cos ^2 x.. Similarly, .f o g(x)=f(g(x))=f(3 x^2).

.=cos (3 x^2).. Note that .3 cos ^2 x ne cos 3 x^2., for .x=0.. Hence, gof .ne f. og.