3. A funciton f:R → R is defined as f(x) = 3x2 +1. Then f-1(x) is : (a) dx-1 (c) f-1 does not exist

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( f=F(x)=3 x^{2}+1 ) ( Rightarrow y=3 x^{2}+1 ) ( Rightarrow y-1=3 x^{2} ) ( Rightarrow x^{2}=frac{y-1}{3} ) ( Rightarrow x=sqrt{frac{y-1}{3}}=f^{-1}(x)=sqrt{frac{y-1}{3}} ) Replaeing at ( y=x ) we get in of ( f(x)} ) ie ( f^{-1}(x)=sqrt{frac{x-1}{3}}, 0 )

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