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Question

If f(x)=3x2 and (gof)1=x2, then g(x) dx is (where C is constant of integration)
  1. 3x222x+C
  2. x2683x+C
  3. x26+83x+C
  4. x22+x+C


Solution

The correct option is C x26+83x+C
f(x)=3x2
Let
y=3x2y+2=3xy+23=x
f1(x)=x+23(gof)1=x2f1(g1(x))=x2f1(g1(x))=x2g1(x)+23=x2g1(x)=3x8g1(x)+83=xg(x)=x+83g(x) dx=x26+83x+C

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