Calculus Examples

$f (x) = \sqrt{x + 2}$ , $g (x) = 8 x^{2} - 14$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (8 x^{2} - 14)$ by substituting in the value of $g$ into $f$ .

$f (8 x^{2} - 14) = \sqrt{(8 x^{2} - 14) + 2}$

Step 3

Add $- 14$ and $2$ .

$f (8 x^{2} - 14) = \sqrt{8 x^{2} - 12}$

Step 4

Factor $4$ out of $8 x^{2} - 12$ .

Tap for more steps...

Step 4.1

Factor $4$ out of $8 x^{2}$ .

$f (8 x^{2} - 14) = \sqrt{4 (2 x^{2}) - 12}$

Step 4.2

Factor $4$ out of $- 12$ .

$f (8 x^{2} - 14) = \sqrt{4 (2 x^{2}) + 4 (- 3)}$

Step 4.3

Factor $4$ out of $4 (2 x^{2}) + 4 (- 3)$ .

$f (8 x^{2} - 14) = \sqrt{4 (2 x^{2} - 3)}$

Step 5

Rewrite $4$ as $2^{2}$ .

$f (8 x^{2} - 14) = \sqrt{2^{2} (2 x^{2} - 3)}$

Step 6

Pull terms out from under the radical.

$f (8 x^{2} - 14) = 2 \sqrt{2 x^{2} - 3}$