Algebra Examples

$f^{- 1} (7) = \frac{x + 4}{6}$

Step 1

Rewrite the equation as $\frac{x + 4}{6} = f^{- 1} \cdot 7$ .

$\frac{x + 4}{6} = f^{- 1} \cdot 7$

Step 2

Multiply both sides of the equation by $6$ .

$6 \frac{x + 4}{6} = 6 (f^{- 1} \cdot 7)$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $6$ .

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Step 3.1.1.1

Cancel the common factor.

$6 \frac{x + 4}{6} = 6 (f^{- 1} \cdot 7)$

Step 3.1.1.2

Rewrite the expression.

$x + 4 = 6 (f^{- 1} \cdot 7)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $6 (f^{- 1} \cdot 7)$ .

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Step 3.2.1.1

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

$x + 4 = 6 (\frac{1}{f} \cdot 7)$

Step 3.2.1.2

Combine $\frac{1}{f}$ and $7$ .

$x + 4 = 6 \frac{7}{f}$

Step 3.2.1.3

Multiply $6 \frac{7}{f}$ .

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Step 3.2.1.3.1

Combine $6$ and $\frac{7}{f}$ .

$x + 4 = \frac{6 \cdot 7}{f}$

Step 3.2.1.3.2

Multiply $6$ by $7$ .

$x + 4 = \frac{42}{f}$

Step 4

Subtract $4$ from both sides of the equation.

$x = \frac{42}{f} - 4$

Step 5

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.

$f (f) = \frac{42}{f} - 4$