Evaluate Using the Given Value f(-9)=2 square root of -9

$f (- 9) = 2 \sqrt{- 9}$

Step 1

Rewrite $- 9$ as $- 1 (9)$ .

$f (- 9) = 2 \sqrt{- 1 \cdot 9}$

Step 2

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$f (- 9) = 2 (\sqrt{- 1} \cdot \sqrt{9})$

Step 3

Rewrite $\sqrt{- 1}$ as $i$ .

$f (- 9) = 2 (i \cdot \sqrt{9})$

Step 4

Rewrite $9$ as $3^{2}$ .

$f (- 9) = 2 (i \cdot \sqrt{3^{2}})$

Step 5

Pull terms out from under the radical, assuming positive real numbers.

$f (- 9) = 2 (i \cdot 3)$

Step 6

Move $3$ to the left of $i$ .

$f (- 9) = 2 (3 \cdot i)$

Step 7

Multiply $3$ by $2$ .

$f (- 9) = 6 i$