Evaluate the Function f(x)=-x^3+2x^2-3 at x=-1

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

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

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

Simplify the result.

Simplify each term.

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

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

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

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

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

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

Add $1$ and $3$ .

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

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

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

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

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

Multiply $2$ by $1$ .

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

Simplify by adding and subtracting.

Add $1$ and $2$ .

$f (- 1) = 3 - 3$

Subtract $3$ from $3$ .

$f (- 1) = 0$

The final answer is $0$ .

$0$