A) \[\{0,\,\,2\}\]
B) \[\left\{ \frac{1}{2},-2 \right\}\]
C) \[\left\{ -\frac{1}{2},2 \right\}\]
D) \[\left\{ \frac{1}{2},2 \right\}\]
Correct Answer: B
Solution :
[b] For \[f(x)=g(x)\Rightarrow 2{{x}^{2}}-1=1-3x\] \[\Rightarrow 2{{x}^{2}}+3x-2=0\Rightarrow 2{{x}^{2}}+4x-x-2=0\] \[\Rightarrow 2x(x+2)-1(x+2)=0\Rightarrow (x+2)(2x-1)=0\] \[\Rightarrow \,\,\,x=-2,\,\,\frac{1}{2}\] \[\therefore \] The domain for which the function \[f(x)=g(x)\] is \[\left\{ -2,\,\,\,\frac{1}{2} \right\}.\]
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