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Question

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

A
2x3
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B
2x+3
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C
2x2+3x+1
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D
2x23x1
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Solution

The correct option is A 2x3
g(x)=x2+x212g(f(x))=2x2+5x+2f2(x)+f(x)2=4x210x+4f2(x)+f(x)(4x210x+6)=0f(x)=1±1+4(4x210x+6)2f(x)=1±1+16x240x+242f(x)=1±(4x5)2=(2x3)

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