Evaluate Using the Given Value f(-x)=(7x^2-1)/(x^2)

$f (- x) = \frac{7 x^{2} - 1}{x^{2}}$

Step 1

Divide each term in $f (- x) = \frac{7 x^{2} - 1}{x^{2}}$ by $- 1 x$ .

$\frac{f (- x)}{- 1 x} = \frac{\frac{7 x^{2} - 1}{x^{2}}}{- 1 x}$

Step 2

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{f (x)}{x} = \frac{\frac{7 x^{2} - 1}{x^{2}}}{- 1 x}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{f x}{x} = \frac{\frac{7 x^{2} - 1}{x^{2}}}{- 1 x}$

Divide $f$ by $1$ .

$f = \frac{\frac{7 x^{2} - 1}{x^{2}}}{- 1 x}$

Step 3

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$f = \frac{7 x^{2} - 1}{x^{2}} \cdot \frac{1}{- 1 x}$

Cancel the common factor of $1$ and $- 1$ .

Rewrite $1$ as $- 1 (- 1)$ .

$f = \frac{7 x^{2} - 1}{x^{2}} \cdot \frac{- 1 (- 1)}{- 1 x}$

Move the negative in front of the fraction.

$f = \frac{7 x^{2} - 1}{x^{2}} (- \frac{1}{x})$

Rewrite using the commutative property of multiplication.

$f = - \frac{7 x^{2} - 1}{x^{2}} \cdot \frac{1}{x}$

Multiply $- \frac{7 x^{2} - 1}{x^{2}} \cdot \frac{1}{x}$ .

Multiply $\frac{1}{x}$ by $\frac{7 x^{2} - 1}{x^{2}}$ .

$f = - \frac{7 x^{2} - 1}{x \cdot x^{2}}$

Multiply $x$ by $x^{2}$ by adding the exponents.

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

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

$f = - \frac{7 x^{2} - 1}{x^{1} x^{2}}$

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

$f = - \frac{7 x^{2} - 1}{x^{1 + 2}}$

Add $1$ and $2$ .

$f = - \frac{7 x^{2} - 1}{x^{3}}$