TS EAMCET · Maths · Functions
The function \(f: C \rightarrow C\) defined by \(f(x)=\frac{a x+d}{c x+d}\) for \(x \in C\) where \(b d \neq 0\) reduces to a constant function, if
- A \(a=c\)
- B \(b=d\)
- C \(a d=b e\)
- D \(a b=c d\)
Answer & Solution
Correct Answer
(C) \(a d=b e\)
Step-by-step Solution
Detailed explanation
\(f(x)=\frac{a x+b}{c x+d}\) ...(i) Now, take option (c) i.e., \(a d=b c\) \(\Rightarrow \quad \frac{a}{b}=\frac{c}{d}=k\) (say) From equation (i), \(\begin{aligned} f(x) & =\frac{b k x+b}{d k x+d} \\ & =\frac{b(k x+1)}{d(k x+1)}=\frac{b}{d}=\text { constant } \end{aligned}\)
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