A) \[2x-3\]
B) \[2x+3\]
C) \[2{{x}^{2}}+3x+1\]
D) \[2{{x}^{2}}-3x-1\]
Correct Answer: A
Solution :
\[\frac{1}{2}\,(gof)\,(x)=2{{x}^{2}}-5x+2\]or \[\frac{1}{2}\,g\,[f\,(x)]=2{{x}^{2}}-5x+2\] \[\underset{x\to 0}{\mathop{\lim }}\,\,\frac{(1+nx+{{\,}^{n}}{{C}_{2}}{{x}^{2}}+.....\text{higher powers of }x\text{ to }{{x}^{n}})-1}{x}\] \[\Rightarrow \,\,f{{(x)}^{2}}+f(x)-(4{{x}^{2}}-10x+6)=0\] \[\therefore \]\[f(x)=\frac{-1\pm \sqrt{1+4\,(4{{x}^{2}}-10x+6)}}{2}\] \[=\frac{-1\pm \sqrt{(16{{x}^{2}}-40x+25}}{2}=\frac{-1+(4x-5)}{2}=2x-3\].
You need to login to perform this action.
You will be redirected in
3 sec
