Evaluate Using the Given Value f(-4) = square root of -4^2+1

$f (- 4) = \sqrt{- 4^{2} + 1}$

Step 1

Simplify the expression.

Raise $4$ to the power of $2$ .

$f (- 4) = \sqrt{- 1 \cdot 16 + 1}$

Multiply $- 1$ by $16$ .

$f (- 4) = \sqrt{- 16 + 1}$

Add $- 16$ and $1$ .

$f (- 4) = \sqrt{- 15}$

Step 2

Rewrite $- 15$ as $- 1 (15)$ .

$f (- 4) = \sqrt{- 1 \cdot 15}$

Step 3

Rewrite $\sqrt{- 1 (15)}$ as $\sqrt{- 1} \cdot \sqrt{15}$ .

$f (- 4) = \sqrt{- 1} \cdot \sqrt{15}$

Step 4

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

$f (- 4) = i \sqrt{15}$