Algebra Examples

$F^{- 1} (x) = \frac{x + 4}{11}$

Step 1

Simplify both sides.

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Step 1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{F} x = \frac{x + 4}{11}$

Step 1.2

Combine $\frac{1}{F}$ and $x$ .

$\frac{x}{F} = \frac{x + 4}{11}$

Step 2

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$x \cdot 11 = F (x + 4)$

Step 3

Solve the equation for $F$ .

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Step 3.1

Rewrite the equation as $F (x + 4) = x \cdot 11$ .

$F (x + 4) = x \cdot 11$

Step 3.2

Divide each term in $F (x + 4) = x \cdot 11$ by $x + 4$ and simplify.

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Step 3.2.1

Divide each term in $F (x + 4) = x \cdot 11$ by $x + 4$ .

$\frac{F (x + 4)}{x + 4} = \frac{x \cdot 11}{x + 4}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $x + 4$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{F (x + 4)}{x + 4} = \frac{x \cdot 11}{x + 4}$

Step 3.2.2.1.2

Divide $F$ by $1$ .

$F = \frac{x \cdot 11}{x + 4}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Move $11$ to the left of $x$ .

$F = \frac{11 x}{x + 4}$

Step 4

To rewrite as a function of $x$ , write the equation so that $F$ is by itself on one side of the equal sign and an expression involving only $x$ is on the other side.

$f (x) = \frac{11 x}{x + 4}$