1.

If g(x) = `x^2+x-2`and `1/2g(f(x)) = 2x^2 -5x+2`, then f(x) isA. 2x-3B. 2x+3C. `2x^(2)+3x+1`D. `2x^(2)-3x-1`

Answer» Correct Answer - A
We have `(1)/(2)"g of "(x)=2x^(2)-5x+2`
`Rightarrow g(f(x))=4x^(2)-10x+4`
`(f(x))^(2)+f(x)-2=4x^(2)-10x+4`
`(f(x))^(2)+f(x)-(4x^(2)-10x+6)=0`
`f(x)=(-1pmsqrt(1+4(4x^(2)-10x+6)))/(2)`
`f(x)=(-1pmsqrt((16x^(2)-40x+25)))/(2)`
`f(x)=(-1pm(4x-5))/(2)=2x-3,-2x+2`
Hence, `f(x)=2x-3`


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