A) \[a=b\]
B) \[c=d\]
C) \[a+b=0\]
D) \[c+d=0\]
Correct Answer: C
Solution :
[c] \[f(x)=\frac{ax+d}{cx+b}\] \[f(f(x))=\frac{a\left( \frac{ax+d}{cx+b} \right)+d}{c\left( \frac{ax+d}{cx+b} \right)+b}=\frac{{{a}^{2}}x+ad+cdx+bd}{cax+cd+bcx+{{b}^{2}}}\] \[f(f(x))=x\Rightarrow \frac{{{a}^{2}}x+ad+cdx+bd}{cax+cd+bcx+{{b}^{2}}}=x\] \[\Rightarrow c(a+b){{x}^{2}}-({{a}^{2}}-{{b}^{2}})x-(a+b)d=0\] \[\Rightarrow (a+b)(c{{x}^{2}}-(a-b)x-d)=0\Rightarrow a+b=0\] As \[c{{x}^{2}}-(a-b)x-d\ne 0\] for all x
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