Let $\mathrm{f}, \mathrm{g}: \mathbf{R} \rightarrow \mathbf{R}$ be defined by $\mathrm{f}(\mathrm{x}

Question

Let $\mathrm{f}, \mathrm{g}: \mathbf{R} \rightarrow \mathbf{R}$ be defined by $\mathrm{f}(\mathrm{x})=\mathrm{x}^3$ and $g(x)=x^2-x+1$.If $A=\{x: f(x)=g(x)\}$, then $\mathrm{n}(\mathrm{A})=$

Professor PC Thomas Classes · Answer

$ \begin{aligned} & \mathrm{f}(\mathrm{x})=\mathrm{g}(\mathrm{x}) \ & \Rightarrow \mathrm{x}^3=\mathrm{x}^2-\mathrm{x}+1 \ & \Rightarrow \mathrm{x}^3-\mathrm{x}^2+\mathrm{x}-1=0 \ & \Rightarrow(\mathrm{x}-1)\left(\mathrm{x}^2+1ight)=0 \ & \Rightarrow \mathrm{x}=1 	ext { as } \mathrm{x} \in \mathbf{R} \end{aligned} $