Find two functions that squeeze a function

Question

The question asks the following:

I'm struggling to set up some relation such that $g(x)≤f(x)≤h(x)$. Specifically, I'm struggling to find $y$-values that either the numerator or denominator of $f(x)$ lies between? Can someone please give me some guidance.

Answer 1

HINT

For example

$$g(x)=\frac{|x|}{x^4+4x^2+8}\to 0$$

$$h(x)=\frac{|x|}{x^4+4x^2+6} \to 0$$

or

$$g(x)=\frac{|x|}{x^2+4x^2+7}=\frac{|x|}{5x^2+7}\to 0$$

$$h(x)=\frac{|x|}{x^4+4x^4+7}=\frac{|x|}{5x^4+7} \to 0$$