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KCET2014MathematicsStatistics

If linear function ( f(x) ) and ( g(x) ) satisfy ( [(3 x-1) x+(1-2 x) x] d x=f(x) x+g(x) x+C ), then

Options

  1. A( f(x)=3 x-5 )
  2. B( g(x)=3+x )
  3. C( f(x)=3(x-1) )
  4. D( g(x)=3(x-1) )

Correct answer

D. ( g(x)=3(x-1) )

Step-by-step solution

Given that I= [(3 x-1) x+(1-2 x) x] d x=f(x) x+g(x) x+c I=(3 x-1) x- x 3 d x+(1-2 x)(- x)+ x(-2) d x=(3 x-1) x+3 x- x+2 x x-2 x+c=(3 x-1-2) x+(2+2 x) x+c=3(x-1) x+2(x+1) x+c Therefore, f(x)=2(x+1) and g(x)=3(x-1)

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