Answer:
[tex]f(g(h(x))) = (\sqrt{x} -6)^4 +4[/tex]
Step-by-step explanation:
Given:
[tex]f(x) = x^4 +4[/tex]
[tex]g(x) = x -6[/tex]
[tex]h(x) = \sqrt{x}[/tex]
Solution:
[tex]f°g°h(x) = f(g(h(x)))[/tex]
We can solve for [tex]g(h(x))[/tex] to make it less complicated.
[tex]g(h(x)) = h(x) -6 \\ g(h(x)) = \sqrt{x} -6[/tex]
Now we can solve for [tex]f(g(h(x)))[/tex].
[tex]f(g(h(x))) = g(h(x))^4 +4 \\ f(g(h(x))) = (\sqrt{x} -6)^4 +4[/tex]
