The domain of the function f(x)= 1 x^ 12 -x^ 9 +x^ 4 -x+1 is given...

$\mathrm{f}(x)$ is defined for $x^{12}-x^{9}+x^{4}-x+1 > 0$$\begin{array}{l} \Rightarrow x^{4}\left(x^{8}+1\right)-x\left(x^{8}+1\right)+1 > 0 \\ \Rightarrow\left(x^{8}+1\right) x\left(x^{3}-1\right)+1 > 0 \end{array}$If $x \geq 1$ or $x \leq-1$, then the above expres - sion is positive. If $-1 < x \leq 0$, the above inequality still holds. If 0 < x < 1$, then\begin{array}{l} x^{12}-x\left(x^{8}+\right)+\left(x^{4}+1\right)>0 \\ \because\left[x^{4}+1>x^{8}+1 \text{ and so } x^{4}+1>x\left(x^{8}+1\right)\right] \end{array}$$$The domain of$ f=(-\infty, \infty)$