Mathematics - Functions Question with Solution | TestHub

$f(x)=\frac{ax+b}{cx+d}$ fof $(x)=\frac{a\left\{\frac{ax+b}{cx+d}\right\}+b}{c\left\{\frac{ax+b}{cx+d}\right\}+d}\Rightarrow \frac{a^{2}x+ab+bcx+bd}{acx+bc+cdx+d^2}=x$ $\Rightarrow (ac+dc)x^2+\left(bc+d^2-bc-a^2\right)x$ $-ab-bd=0,\forall x\in R$ $\Rightarrow (a+d)c=0,d^2-a^2=0$ and $(a+d)b=0$ $\Rightarrow a+d=0$