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$If g (x) = x^{2} + x - 2 and \frac{1}{2} (gof) (x) = 2 x^{2} - 5 x + 2, then f (x) is equal to$

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2x-3

2x+3

2x2+3x+1

2x2−3x−1

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Correct option is A

gx=x2+x-2 and gofx =4x2-10x+4 ⇒gfx=fx2+fx-2 = 4x2-10x+4 fx2 +fx-4x2-10x+6=0⇒ fx=-1±16x2-40x+252=-1±4x-52 =2x-3 or -2x+2 hence fx=2x-3

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If g(x)=x2+x−2 and 12( gof )(x)=2x2−5x+2 , then f(x) is equal to

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Ready to Test Your Skills?

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$If g (x) = x^{2} + x - 2 and \frac{1}{2} (gof) (x) = 2 x^{2} - 5 x + 2, then f (x) is equal to$