Answer:
[tex]h(x)=-2x+4[/tex]
[tex]g(x)=\sqrt[3]{x}-5[/tex]
Step-by-step explanation:
Consider the given function is
[tex]f(x)=\sqrt[3]{-2x+4}-5[/tex]
It is given that [tex]f(x)=g(h(x))[/tex] and neither g(x) nor h(x) is solely x.
[tex]f(x)=\sqrt[3]{(-2x+4)}-5[/tex]
Let [tex]h(x)=-2x+4[/tex], then we get
[tex]f(x)=g(h(x))=\sqrt[3]{h(x)}-5[/tex]
Substitute h(x)=x in the above function.
[tex]g(x)=\sqrt[3]{x}-5[/tex]
Therefore, the required functions are [tex]h(x)=-2x+4[/tex] and [tex]g(x)=\sqrt[3]{x}-5[/tex].
Check the solutions.
[tex]g(h(x))=g(-2x+4)[/tex] [tex][\because h(x)=-2x+4][/tex]
[tex]g(h(x))=\sqrt[3]{-2x+4}-5[/tex] [tex][\because g(x)=\sqrt[3]{x}-5][/tex]
[tex]g(h(x))=f(x)[/tex]
Therefore, our solution is correct.
