step by step solution:

The given function is:

g(x)=x^{5}-9x^{3}

We want to solve for

g(x)\gt0

on Substituting the value of the given function into the inequality we get

\textcolor{primary}{x^{5}-9x^{3}}\gt0

Solve the inequality for x:

x^3(x^2-9)>0

x^3(x-3)(x+3)>0

now we can conclude that the solution of x will be :

x\in(-3,0)\cup(3,\infty)

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