Question 1092039
<br>There are many ways to do this.  Two easy, but not very useful, ways are these:
{{{g(x) = 4/x^2+9}}}  and  {{{f(x) = x}}}<br>
or
{{{g(x) = x}}}  and  {{{f(x) = 4/x^2+9}}}<br>
In both of those examples, one of the functions does nothing to the input and the other does everything.  But in both cases you get the right result:
{{{f(g(x)) = 4/x^2+9}}}<br>
To get a meaningful way to get the expression as the composition of two functions, think about how you would go about evaluating the expression for a given value of x.  Probably, you would first divide 4 by the square of the input; and then you would add 9.  So make those two operations your two functions:<br>
{{{g(x) = 4/x^2}}}  and  {{{f(x) = x+9}}}<br>
That would give you
{{{f(g(x)) = (4/x^2)+9 = 4/x^2+9}}}<br>
While it is far less likely, you might notice that 4/x^2 is (2/x)^2; so you could define the two functions as<br>
{{{g(x) = 2/x)}}}  and  {{{f(x) = x^2+9}}}<br>
That would give you
{{{f(g(x)) = (2/x)^2+9 = 4/x^2+9}}}<br>
And there are probably other less obvious and more complicated ways to get the desired function as a composition of two functions.