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 $x$ .

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Step 3.1

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

$11 x = f (x + 4)$

Step 3.2

Simplify $f (x + 4)$ .

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Step 3.2.1

Apply the distributive property.

$11 x = f x + f \cdot 4$

Step 3.2.2

Move $4$ to the left of $f$ .

$11 x = f x + 4 f$

Step 3.3

Subtract $f x$ from both sides of the equation.

$11 x - f x = 4 f$

Step 3.4

Factor $x$ out of $11 x - f x$ .

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Step 3.4.1

Factor $x$ out of $11 x$ .

$x \cdot 11 - f x = 4 f$

Step 3.4.2

Factor $x$ out of $- f x$ .

$x \cdot 11 + x (- f) = 4 f$

Step 3.4.3

Factor $x$ out of $x \cdot 11 + x (- f)$ .

$x (11 - f) = 4 f$

Step 3.5

Divide each term in $x (11 - f) = 4 f$ by $11 - f$ and simplify.

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Step 3.5.1

Divide each term in $x (11 - f) = 4 f$ by $11 - f$ .

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

Step 3.5.2

Simplify the left side.

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Step 3.5.2.1

Cancel the common factor of $11 - f$ .

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Step 3.5.2.1.1

Cancel the common factor.

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

Step 3.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{4 f}{11 - f}$

Step 4

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

$f (f) = \frac{4 f}{11 - f}$