Algebra Examples

$f (x) = - x^{3} - 4 x - 2$ at $x = - 1$

Step 1

Replace the variable $x$ with $- 1$ in the expression.

$f (- 1) = - {(- 1)}^{3} - 4 \cdot - 1 - 2$

Step 2

Simplify the result.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $- 1$ by ${(- 1)}^{3}$ by adding the exponents.

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Step 2.1.1.1

Multiply $- 1$ by ${(- 1)}^{3}$ .

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Step 2.1.1.1.1

Raise $- 1$ to the power of $1$ .

$f (- 1) = (- 1) {(- 1)}^{3} - 4 \cdot - 1 - 2$

Step 2.1.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$f (- 1) = {(- 1)}^{1 + 3} - 4 \cdot - 1 - 2$

Step 2.1.1.2

Add $1$ and $3$ .

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

Step 2.1.2

Raise $- 1$ to the power of $4$ .

$f (- 1) = 1 - 4 \cdot - 1 - 2$

Step 2.1.3

Multiply $- 4$ by $- 1$ .

$f (- 1) = 1 + 4 - 2$

Step 2.2

Simplify by adding and subtracting.

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Step 2.2.1

Add $1$ and $4$ .

$f (- 1) = 5 - 2$

Step 2.2.2

Subtract $2$ from $5$ .

$f (- 1) = 3$

Step 2.3

The final answer is $3$ .

$3$

Step 3