QuestionEvaluate $(f \circ g)(6)$ for $f(x)=\sqrt{x+28}$ and $g(x)=x^{2}$ . What is the simplified result?

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is $\sqrt{x+28}$ . The function $g(x)$ is $x^{}$
3. We need to find the value of $(f \circ g)(6)$

STEP 2

The notation $(f \circ g)(6)$ represents the composition of the functions $f$ and $g$ , evaluated at $x=6$ . This means we first apply the function $g$ to $6$ , then apply the function $f$ to the result. $(f \circ g)(6) = f(g(6))$

STEP 3

First, we need to evaluate $g(6)$ . We do this by substituting $x=6$ into the function $g(x)$ .
$g(6) = (6)^{2}$

STEP 4

Calculate the value of $g(6)$ .
$g(6) = (6)^{2} =36$

STEP 5

Now that we have the value of $g()$ , we can substitute this into the function $f(x)$ to find the value of $(f \circ g)()$ .
$(f \circ g)() = f(g()) = f(36)$

STEP 6

Substitute $x=36$ into the function $f(x)$ .
$f(36) = \sqrt{36+28}$

STEP 7

Calculate the value of $f(36)$ .
$f(36) = \sqrt{36+28} = \sqrt{64}$

STEP 8

implify the square root.
$f(36) = \sqrt{64} =8$ So, the value of $(f \circ g)(6)$ is8.

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