A) c and d both arbitrary
B) \[c=1,\ d\] arbitrary
C) c arbitrary, \[d=1\]
D) \[c=1,\ d=1\]
Correct Answer: B
Solution :
\[(fog)(x)=f(g(x))=a(cx+d)+b\] and \[(gof)(x)=g(f(x))=c(ax+b)+d\] Given that, \[(fog)(x)=(gof)(x)\] and at \[a=1,\,b=2\] Þ \[\underset{x\to 0}{\mathop{\lim }}\,\,\,3\,\frac{\tan 3x}{3x}+\underset{x\to 0}{\mathop{\lim }}\,\cos x=3+1=4\] Þ \[c=1\] and d is arbitrary.
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