Evaluate the Function f(x)=(x^7)/7-7/(x^7) at x=-1

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

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

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

Simplify the result.

Simplify each term.

Raise $- 1$ to the power of $7$ .

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

Move the negative in front of the fraction.

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

Raise $- 1$ to the power of $7$ .

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

Divide $7$ by $- 1$ .

$f (- 1) = - \frac{1}{7} + 7$

Multiply $- 1$ by $- 7$ .

$f (- 1) = - \frac{1}{7} + 7$

To write $7$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$f (- 1) = - \frac{1}{7} + 7 \cdot \frac{7}{7}$

Combine $7$ and $\frac{7}{7}$ .

$f (- 1) = - \frac{1}{7} + \frac{7 \cdot 7}{7}$

Combine the numerators over the common denominator.

$f (- 1) = \frac{- 1 + 7 \cdot 7}{7}$

Simplify the numerator.

Multiply $7$ by $7$ .

$f (- 1) = \frac{- 1 + 49}{7}$

Add $- 1$ and $49$ .

$f (- 1) = \frac{48}{7}$

The final answer is $\frac{48}{7}$ .

$\frac{48}{7}$

The result can be shown in multiple forms.

Exact Form:

$\frac{48}{7}$

Decimal Form:

$6.\overline{857142}$

Mixed Number Form:

$6 \frac{6}{7}$