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Kaylis [27]
3 years ago
12

How do I even start this? And how to i order the equation to solve

Mathematics
1 answer:
Kobotan [32]3 years ago
6 0

f(g(h(x)))=f(g(\sqrt x))=f(\sqrt x-1)=\boxed{(\sqrt x-1)^4+4}

This is because

h(x)=\sqrt x

g(x)=x-1

\implies g(h(x))=\sqrt x-1

(that is, replace any instance of <em>x</em> in the definition of <em>g</em> with √<em>x</em> )

and

f(x)=x^4+4

\implies f(\sqrt x-1)=(\sqrt x-1)^4+4

(replace any <em>x</em> in <em>f</em> with √<em>x</em> - 1)

Also acceptable:

(\sqrt x-1)^4+4=((\sqrt x)^4-4(\sqrt x)^3+6(\sqrt x)^2-4\sqrt x+1)+4

=\boxed{x^2-4x\sqrt x+6x-4\sqrt x+5}

(assuming <em>x</em> is not negative)

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