A) \[2x-3\]
B) \[2x+3\]
C) \[2{{x}^{2}}+3x+1\]
D) \[2{{x}^{2}}-3x-1\]
Correct Answer: A
Solution :
[a] \[g(x)={{x}^{2}}+x-2\] and \[\frac{1}{2}(gof)(x)=2{{x}^{2}}-5x+2\] \[\Rightarrow g(f(x))=4{{x}^{2}}-10x+4\Rightarrow {{(f(x))}^{2}}+f(x)-2\] \[=4{{x}^{2}}-10x+4\] \[\Rightarrow {{(f(x))}^{2}}+f(x)-(4{{x}^{2}}-10x+6)=0\] \[\Rightarrow f(x)=\frac{-1\pm \sqrt{16{{x}^{2}}-40x+25}}{2}\] \[=\frac{-1\pm (4x-5)}{2}\] \[=\frac{4x-6}{2}\]or \[\frac{-4x+4}{2}=2x-3,\] or \[-2x+2\] Hence \[f(x)=2x-3.\]
You need to login to perform this action.
You will be redirected in
3 sec
