We have the following functions
[tex]\begin{gathered} f(x)=\sqrt[]{x}=x^{\frac{1}{2}} \\ g(x)=(\sqrt[]{x})^3=x^{\frac{3}{2}} \end{gathered}[/tex]
We want to find:
[tex]h(x)=(fg)(x)=f(x)\times g(x)[/tex]
If we substitute and do the product:
[tex]f(x)\times g(x)=x^{1/2}\times x^{3/2}=x^{(1/2+3/2)}=x^{4/2}=x^2[/tex]
Our h(x) function is:
[tex]h(x)=x^2[/tex]
We still need to be careful about the domain. The restrictions from the f(x) and g(x) function remains, then the function h(x) will be defined only for
x >= 0.
[tex]h(x)=x^2,x\ge0[/tex]
