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

$f (- x) = \frac{3 {(- x)}^{2} - 1}{{(- x)}^{2}}$

Step 1

Simplify the numerator.

Apply the product rule to $- x$ .

$f (- x) = \frac{3 ({(- 1)}^{2} x^{2}) - 1}{{(- x)}^{2}}$

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

$f (- x) = \frac{3 (1 x^{2}) - 1}{{(- x)}^{2}}$

Multiply $x^{2}$ by $1$ .

$f (- x) = \frac{3 x^{2} - 1}{{(- x)}^{2}}$

Step 2

Simplify the denominator.

Apply the product rule to $- x$ .

$f (- x) = \frac{3 x^{2} - 1}{{(- 1)}^{2} x^{2}}$

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

$f (- x) = \frac{3 x^{2} - 1}{1 x^{2}}$

Multiply $x^{2}$ by $1$ .

$f (- x) = \frac{3 x^{2} - 1}{x^{2}}$

Step 3