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Solved on Jan 23, 2024

Evaluate $f(-1)$ and solve $f(x)=3$ for the function $f(x)=\sqrt{x+5}$ .

STEP 1

Assumptions
1. The function given is $f(x)=\sqrt{x+5}$ .
2. For part a, we need to evaluate $f(-1)$ .
3. For part b, we need to solve the equation $f(x)=3$ for $x$ .

STEP 2

To evaluate $f(-1)$ , we substitute $x$ with $-1$ in the function $f(x)$ .
$f(-1) = \sqrt{-1+5}$

STEP 3

Perform the arithmetic inside the square root.
$f(-1) = \sqrt{4}$

STEP 4

Calculate the square root.
$f(-1) = 2$
For part a, $f(-1) = 2$ .

STEP 5

Now, for part b, we need to solve the equation $f(x) = 3$ . We substitute $f(x)$ with $\sqrt{x+5}$ .
$\sqrt{x+5} = 3$

STEP 6

To solve for $x$ , we need to square both sides of the equation to eliminate the square root.
$(\sqrt{x+5})^2 = 3^2$

STEP 7

Simplify both sides of the equation.
$x+5 = 9$

STEP 8

Subtract 5 from both sides of the equation to solve for $x$ .
$x = 9 - 5$

STEP 9

Calculate the value of $x$ .
$x = 4$
For part b, $x = 4$ .

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