The function $f: C ightarrow C$ defined by $f(x)=\frac{a x+d}{c x+d}$ for $x \in C$ where $b d
eq 0$ reduces to a constant function, if

Question

The function $f: C ightarrow C$ defined by $f(x)=\frac{a x+d}{c x+d}$ for $x \in C$ where $b d 
eq 0$ reduces to a constant function, if

Aicharya · Accepted Answer

Now, take option (c) i.e., $a d=b c$ $\Rightarrow \quad \frac{a}{b}=\frac{c}{d}=k$ (say) From equation (i), $\begin{aligned} f(x) & =\frac{b k x+b}{d k x+d} \\ & =\frac{b(k x+1)}{d(k x+1)}=\frac{b}{d}=\text { constant } \end{aligned}$

The function $f: C \rightarrow C$ defined by $f(x)=\frac{a x+d}{c x+d}$ for $x \in C$ where $b d \neq 0$…

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