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

Options

A. `2x-3`
B. `-2x+2`
C. `x-3`
D. None of these

Answer

C

Explanation

`(1)/(2)(gof)(x)=2x^(2)-5x+2`
` or (1)/(2)g[f(x)]=2x^(2)-5x+2`
` :. [{f(x)}^(2)+{f(x)}-2]=2[2x^(2)-5x+2]`
` or f(x)^(2)+f(x)-(4x^(2)-10x+6)=0`
` :. f(x)=(-1+-sqrt(1+4(4x^(2)-10x+6)))/(2)`
`=(-1+-sqrt((16x^(2)-40x+25)))/(2)=(-1+-(4x-5))/(2)`
`=2x-3 or -2x+2`