MHT CET20243 May 2024Morning ShiftMathematicsFunctionsActual

If g (x)=x^2+x-1 and (gof) (x)=4 x^2-10 x+5 , then f (2) is equal to

Options

Correct answer

D. -2

Step-by-step solution

If g(x)=x^2+x-1 and (g f)(x)=4 x^2-10 x+5 , then f(2) ? 1. Relationship: g(f(x))=4 x^2-10 x+5 2. Substitute g(x) : Given g(x)=x^2+x-1 , substitute f(x) : (f(x))^2+f(x)-1=4 x^2-10 x+5 3. Solve for f(x) : Use quadratic identities to isolate f(x) . Substitute x=2 . After simplifications: Answer: -2, Option 4.

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