Calculus Examples

$f (x) = \sqrt{x + 2}$ , $g (x) = x^{2} - 1$ , $(f - g) (x)$

Step 1

Evaluate $f - g$ .

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Step 1.1

Replace the function designators in $f - g$ with the actual functions.

$(\sqrt{x + 2}) - (x^{2} - 1)$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$\sqrt{x + 2} - x^{2} - - 1$

Step 1.2.2

Multiply $- 1$ by $- 1$ .

$\sqrt{x + 2} - x^{2} + 1$

Step 1.3

Reorder $\sqrt{x + 2}$ and $- x^{2}$ .

$- x^{2} + \sqrt{x + 2} + 1$

Step 2

Evaluate $f - g$ at $x$ .

$- {(x)}^{2} + \sqrt{(x) + 2} + 1$

Step 3

Simplify $- {(x)}^{2} + \sqrt{(x) + 2} + 1$ .

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Step 3.1

Remove parentheses.

$- {(x)}^{2} + \sqrt{(x) + 2} + 1$

Step 3.2

Remove parentheses.

$- x^{2} + \sqrt{x + 2} + 1$