If g(x)=x2+x−2 and 12gof(x)=2x2+5x+2, then f(x) is
A
2x−3
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B
2x+3
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C
2x2+3x+1
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D
2x2−3x−1
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Solution
The correct option is A2x−3 g(x)=x2+x−212g(f(x))=2x2+5x+2⇒f2(x)+f(x)−2=4x2−10x+4⇒f2(x)+f(x)−(4x2−10x+6)=0f(x)=−1±√1+4(4x2−10x+6)2f(x)=−1±√1+16x2−40x+242f(x)=−1±(4x−5)2=(2x−3)