Let f$($x$)=7$x$4+3$x$3+64$x$2+81$x $+16.$ and g$($x$)=$ x$4.$ Show that f$($x$)$ is O$($g$($x$))$ directly by using the precise definition of big O from lecture. Also please follow the format of the example given in lecture. Structure your proof in such a way that each term of the polynomial is bounded by a whole number multiplied by x$4,$ for suitably large x$.$s was done in lecture, please choose your whole number to be as small as possible, then figure out the required condition for how large x needs to be$.$ For example, the inequality $5$x$31$x$4$ would be true for all x $5.$ In that case the whole number is $1.($The only smaller whole number would be $0$ and it's certainly not true that $5$x$30$x$4$ for any large values of x whatsoever.$)$Please watch the recorded lecture before doing this problem so you do it correctly.