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

Studdy Solution

STEP 1

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

STEP 2

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

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

To solve for xx, we need to square both sides of the equation to eliminate the square root.
(x+5)2=32(\sqrt{x+5})^2 = 3^2

STEP 7

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

STEP 8

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

STEP 9

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

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