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BITSAT2022MathematicsFunctionsActual

If g(x)=x^2+x-2 and 1 2 g o f(x)=2 x^2-5 x+2 then f(x) is equal to

Options

  1. A2 x-3
  2. B2 x+3
  3. C2 x^2+3 x+1
  4. D2 x^2-3 x+1

Correct answer

A. 2 x-3

Step-by-step solution

We have, 1 2 go f(x)=2 x^2-5 x+2 aligned & g(f(x))=4 x^2-10 x+4 & (f(x))^2+f(x)-2=4 x^2-10 x+4 & (f(x))^2+f(x)- (4 x^2-10 x+6 )=0 & f(x)= -1 1+4 (4 x^2-10 x+6 ) 2 & f(x)= -1 16 x^2-40 x+25 2 & f(x)= -1 (4 x-5) 2 =2 x-3,-2 x+2 aligned Hence, f(x)=2 x-3

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