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If g(x)=x^2+x-2a n d1/2gof(x)=2x^2-5x+2,...

If `g(x)=x^2+x-2a n d1/2gof(x)=2x^2-5x+2,` then which is not a possible `f(x)?` `2x-3` (b) `-2x+2` `x-3` (d) None of these

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Given,
`1/2gof(x)=2x^2-5x+2,`
`=>1/2g[f(x)]=2x^2-5x+2`
also `g(x)=x^2+x-2`
so,`[f(x)^2+f(x)-2]=2[2x^2-5x+2]`
`=>f(x)^2+f(x)-(4x^2-10x-6)`
`=>f(x)=(-1pmsqrt(1+4(4x^2-10x=6)))/2`
`=(-1pm(4x-5))/2`
`=2x-3` or `-2x+2`
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