Let $g (x) = x + 6$ . Find $f (x)$ so that $h (x) = (f \circ g) (x)$ .
$h (x) = \sqrt{x + 6} + 5$
$f (x) =$

Answer

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Answer

The final answer is $f (x) = \sqrt{x} + 5$

Steps

Step 1 ：Given that $h (x) = (f \circ g) (x) = \sqrt{x + 6} + 5$ , we want to find $f (x)$ .

Step 2 ：We know that $g (x) = x + 6$ , so we can substitute $g (x)$ into $h (x)$ to get $h (g (x)) = \sqrt{g (x) + 6} + 5$

Step 3 ：Since $h (x) = (f \circ g) (x)$ , we can equate $h (g (x))$ and $h (x)$ to find $f (x)$

Step 4 ：So, $f (x) = \sqrt{x + 6} + 5$

Step 5 ：Therefore, $f (x) = \sqrt{x} + 5$

Step 6 ：Checking our result, we substitute $f (x)$ into $h (x)$ to get $h (x) = \sqrt{g (x) + 6} + 5 = \sqrt{x + 6} + 5$ , which is the original equation.

Step 7 ：So, our result is correct.

Step 8 ：The final answer is $f (x) = \sqrt{x} + 5$

Let g(x)=x+6. Find f(x) so that h(x)=(f∘g)(x).h(x)=x+6+5f(x)=

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Let $g (x) = x + 6$ . Find $f (x)$ so that $h (x) = (f \circ g) (x)$ .
$h (x) = \sqrt{x + 6} + 5$
$f (x) =$