Precalculus Examples

$f (x) = 1 - x^{2}$ , $g (x) = x + 1$ , $(f - g) (0)$

Step 1

Evaluate $f - g$ .

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Step 1.1

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

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

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$1 - x^{2} - x - 1 \cdot 1$

Step 1.2.2

Multiply $- 1$ by $1$ .

$1 - x^{2} - x - 1$

Step 1.3

Combine the opposite terms in $1 - x^{2} - x - 1$ .

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Step 1.3.1

Subtract $1$ from $1$ .

$- x^{2} - x + 0$

Step 1.3.2

Add $- x^{2} - x$ and $0$ .

$- x^{2} - x$

Step 2

Evaluate $f - g$ at $0$ .

$- {(0)}^{2} - (0)$

Step 3

Simplify $- {(0)}^{2} - (0)$ .

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Step 3.1

Remove parentheses.

$- {(0)}^{2} - (0)$

Step 3.2

Raising $0$ to any positive power yields $0$ .

$- 0 - (0)$

Step 3.3

Multiply $- 1$ by $0$ .

$0 - (0)$

Step 3.4

Subtract $0$ from $0$ .

$0$