Evaluate the Function f(x)=2x^3-9x^2+12x-5 at x=-1

$f (x) = 2 x^{3} - 9 x^{2} + 12 x - 5$ at $x = - 1$

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

$f (- 1) = 2 {(- 1)}^{3} - 9 {(- 1)}^{2} + 12 (- 1) - 5$

Simplify the result.

Simplify each term.

Raise $- 1$ to the power of $3$ .

$f (- 1) = 2 \cdot - 1 - 9 {(- 1)}^{2} + 12 (- 1) - 5$

Multiply $2$ by $- 1$ .

$f (- 1) = - 2 - 9 {(- 1)}^{2} + 12 (- 1) - 5$

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

$f (- 1) = - 2 - 9 \cdot 1 + 12 (- 1) - 5$

Multiply $- 9$ by $1$ .

$f (- 1) = - 2 - 9 + 12 (- 1) - 5$

Multiply $12$ by $- 1$ .

$f (- 1) = - 2 - 9 - 12 - 5$

Simplify by subtracting numbers.

Subtract $9$ from $- 2$ .

$f (- 1) = - 11 - 12 - 5$

Subtract $12$ from $- 11$ .

$f (- 1) = - 23 - 5$

Subtract $5$ from $- 23$ .

$f (- 1) = - 28$

The final answer is $- 28$ .

$- 28$