Algebra Examples

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

Step 1

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

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

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 $1$ .

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

Step 2.1.1.1.2

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

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

Step 2.1.1.2

Add $1$ and $3$ .

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

Step 2.1.2

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

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

Step 2.1.3

Raise $- 1$ to the power of $2$ .

$f (- 1) = 1 + 2 \cdot 1 - 3$

Step 2.1.4

Multiply $2$ by $1$ .

$f (- 1) = 1 + 2 - 3$

Step 2.2

Simplify by adding and subtracting.

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Step 2.2.1

Add $1$ and $2$ .

$f (- 1) = 3 - 3$

Step 2.2.2

Subtract $3$ from $3$ .

$f (- 1) = 0$

Step 2.3

The final answer is $0$ .

$0$

Step 3