A) \[\frac{x+5}{2x-1},\ x\ne \frac{1}{2}\]
B) \[\frac{5x+1}{2-x},\ x\ne 2\]
C) \[\frac{5x-1}{2-x},\ x\ne 2\]
D) \[\frac{x-5}{2x+1},\ x\ne \frac{1}{2}\]
Correct Answer: B
Solution :
Let \[f(x)=y\]Þ \[x={{f}^{-1}}(y)\]. Now,\[y=\frac{2x-1}{x+5},(x\ne -5)\] \[xy+5y=2x-1\Rightarrow 5y+1=2x-xy\]. Þ \[x(2-y)=5y+1\Rightarrow x=\frac{5y+1}{2-y}\] Þ \[{{f}^{-1}}(y)=\frac{5y+1}{2-y}\] \ \[{{f}^{-1}}(x)=\frac{5x+1}{2-x},\,\,x\ne 2\].
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