If $$ h(x)=g(f(x)) $$, and $$ h(x)=\sqrt{5 x+2} $$, give $$ g(u) $$, the outer function, and $$ u=f(x) $$, the inner function. $$ g(u)=\square $$ (use $$ u $$ as the variable) $$ u=f(x)=\square $$ (use $$ x $$ as the variable)

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We are given that  
$$
h(x)=g(f(x))=\sqrt{5x+2}.
$$  
This means that the composition of the functions $$ g $$ (outer) and $$ f $$ (inner) is equal to $$ \sqrt{5x+2} $$.

**Step 1.**  
Identify the inner function $$ f(x) $$. To get the expression inside the square root, we set  
$$
u = f(x) = 5x + 2.
$$

**Step 2.**  
Now express the outer function $$ g(u) $$ such that when we substitute $$ u = f(x) $$ into it, we recover $$ \sqrt{5x+2} $$. Since  
$$
h(x)=\sqrt{5x+2} = \sqrt{f(x)},
$$  
we define the outer function as  
$$
g(u)=\sqrt{u}.
$$

Thus, the solutions are:  
$$
g(u)=\sqrt{u} \quad \text{and} \quad u=f(x)=5x+2.
$$
$$ g(u) = \sqrt{u} $$ $$ u = f(x) = 5x + 2 $$

If , and
,
give , the outer function, and , the inner function.
(use as the variable)
(use as the variable)

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