Solve for x F(x)=1/x

$F (x) = \frac{1}{x}$

Step 1

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$1, x$

The LCM of one and any expression is the expression.

$x$

Step 2

Multiply each term in $F x = \frac{1}{x}$ by $x$ to eliminate the fractions.

Multiply each term in $F x = \frac{1}{x}$ by $x$ .

$F x \cdot x = \frac{1}{x} x$

Simplify the left side.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$F (x \cdot x) = \frac{1}{x} x$

Multiply $x$ by $x$ .

$F x^{2} = \frac{1}{x} x$

Simplify the right side.

Cancel the common factor of $x$ .

Cancel the common factor.

$F x^{2} = \frac{1}{x} x$

Rewrite the expression.

$F x^{2} = 1$

Step 3

Solve the equation.

Divide each term in $F x^{2} = 1$ by $F$ and simplify.

Divide each term in $F x^{2} = 1$ by $F$ .

$\frac{F x^{2}}{F} = \frac{1}{F}$

Simplify the left side.

Cancel the common factor of $F$ .

Cancel the common factor.

$\frac{F x^{2}}{F} = \frac{1}{F}$

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

$x^{2} = \frac{1}{F}$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{\frac{1}{F}}$

Simplify $\pm \sqrt{\frac{1}{F}}$ .

Rewrite $\sqrt{\frac{1}{F}}$ as $\frac{\sqrt{1}}{\sqrt{F}}$ .

$x = \pm \frac{\sqrt{1}}{\sqrt{F}}$

Any root of $1$ is $1$ .

$x = \pm \frac{1}{\sqrt{F}}$

Multiply $\frac{1}{\sqrt{F}}$ by $\frac{\sqrt{F}}{\sqrt{F}}$ .

$x = \pm \frac{1}{\sqrt{F}} \cdot \frac{\sqrt{F}}{\sqrt{F}}$

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt{F}}$ by $\frac{\sqrt{F}}{\sqrt{F}}$ .

$x = \pm \frac{\sqrt{F}}{\sqrt{F} \sqrt{F}}$

Raise $\sqrt{F}$ to the power of $1$ .

$x = \pm \frac{\sqrt{F}}{{\sqrt{F}}^{1} \sqrt{F}}$

Raise $\sqrt{F}$ to the power of $1$ .

$x = \pm \frac{\sqrt{F}}{{\sqrt{F}}^{1} {\sqrt{F}}^{1}}$

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

$x = \pm \frac{\sqrt{F}}{{\sqrt{F}}^{1 + 1}}$

Add $1$ and $1$ .

$x = \pm \frac{\sqrt{F}}{{\sqrt{F}}^{2}}$

Rewrite ${\sqrt{F}}^{2}$ as $F$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{F}$ as $F^{\frac{1}{2}}$ .

$x = \pm \frac{\sqrt{F}}{{(F^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x = \pm \frac{\sqrt{F}}{F^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$x = \pm \frac{\sqrt{F}}{F^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x = \pm \frac{\sqrt{F}}{F^{\frac{2}{2}}}$

Rewrite the expression.

$x = \pm \frac{\sqrt{F}}{F^{1}}$

Simplify.

$x = \pm \frac{\sqrt{F}}{F}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = \frac{\sqrt{F}}{F}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \frac{\sqrt{F}}{F}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = \frac{\sqrt{F}}{F}$

$x = - \frac{\sqrt{F}}{F}$

$x = \frac{\sqrt{F}}{F}$

$x = - \frac{\sqrt{F}}{F}$

$x = \frac{\sqrt{F}}{F}$

$x = - \frac{\sqrt{F}}{F}$

Solve for x F(x)=1/x

Related Questions

Support LCMGCF.com by disabling your adblocker.