Mathematics - Functions Question with Solution | TestHub

$\mathrm{f}(x)$ 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 $x\ge 1$ or $x\le -1$, then the above expres - sion is positive. If $-1<x\le 0$, 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 $f=(-\infty ,\infty )$