Let f(x)=sinx , g(x)=ln|x| . if the range of composite function fg(x) and gf(x) are R1 , and R2 respectively , then

Answers (1)

Solution:    f[g(x)]=sin (ln left | x 
ight |)

          Rightarrow     D_1=R-�\Rightarrow R_1=[-1,1]

       Similarly   g[f(x)]=ln left | sin x 
ight |

                     D_2=R-
pi,    forall   n in Z.

        ecause     0leq left | sin x 
ight |leq 1   and  ln x  is not defined for xleq 0.

       	herefore       -infty < ln left | sin x 
ight |leq 0   i.e R_2=(-infty ,0].

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