A) \[{{f}^{-1}}(x)=-f(x)\]
B) \[f\,of\left( x \right)=f\left( x \right)\]
C) \[{{f}^{-1}}(x)=-f(x)\]
D) \[{{f}^{-1}}(x)=\frac{1}{20}f(x)\]
Correct Answer: C
Solution :
[c] \[\because f(x)=\frac{3x+1}{5x-3}\Rightarrow \,y=\frac{3x+2}{5x-3}\] \[5y.x-3y=3x+2x\left( 5y-3 \right)=3y+2\] \[x=\frac{3y+2}{5y-3}.\,\,\] \[\therefore Hence\,{{f}^{-1}}(x)=f(x).\] Option [c] is correct.
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