A) \[2x-3\]
B) \[-2x+2\]
C) \[x-3\]
D) None of these
Correct Answer: C
Solution :
[c] \[\frac{1}{2}(gof)(x)=2{{x}^{2}}-5x+2\] Or \[\frac{1}{2}g[f(x)]=2{{x}^{2}}-5x+2\] \[\therefore [{{\{f(x)\}}^{2}}+\{f(x)\}-2]=[2{{x}^{2}}-5x+2]\] Or \[f{{(x)}^{2}}+f(x)-(4{{x}^{2}}-10x+6)=0\] \[\therefore f(x)=\frac{-1\pm \sqrt{1+4(4{{x}^{2}}-10x+6)}}{2}\] \[=\frac{-1\pm \sqrt{(16{{x}^{2}}-40x+25)}}{2}=\frac{-1\pm (4x-5)}{2}\] \[=2x-3\] or \[-2x+2\]
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