functions

\hspace{-16}$may be op want to ask Domain of $\bf{f(x)=\sqrt{x^{12}-x^9+x^4-x+1}}$\\\\\\ \underline{\underline{Solution\;\;::}}\;\; If $\bf{f(x)}$ id defined then $\bf{x^{12}-x^9+x^4-x+1\geq 0}$\\\\\\ Now we will check for diff. Interval whether this expression is $\bf{\geq 0}$ or not.\\\\\\ $\bullet$ If $\bf{x\leq 0.}$ Then $\bf{x^{12}-x^9+x^4-x+1>0}$\\\\\\ $\bullet$ If $\bf{0<x\leq 1.}$ Then $\bf{+x^{12}+x^4.(1-x^5)+(1-x)>0}$\\\\\\ $\bullet$ If $\bf{x>1.}$ Then $\bf{x^9.(x^3-1)+x.(x^3-1)+1>0}$\\\\\\ So we have seen that $\bf{x^{12}-x^9+x^4-x+1>0\;\forall \;x\in \mathbb{R}}$\\\\\\ So Domain of $\bf{f(x)=\sqrt{x^{12}-x^9+x^4-x+1}}$ is all Real no.