Find the Inverse F(x)=7x

$F (x) = 7 x$

Step 1

Write $F (x) = 7 x$ as an equation.

$y = 7 x$

Step 2

Interchange the variables.

$x = 7 y$

Step 3

Solve for $y$ .

Rewrite the equation as $7 y = x$ .

$7 y = x$

Divide each term in $7 y = x$ by $7$ and simplify.

Divide each term in $7 y = x$ by $7$ .

$\frac{7 y}{7} = \frac{x}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{x}{7}$

Divide $y$ by $1$ .

$y = \frac{x}{7}$

Step 4

Replace $y$ with $F^{- 1} (x)$ to show the final answer.

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

Step 5

Verify if $F^{- 1} (x) = \frac{x}{7}$ is the inverse of $F (x) = 7 x$ .

To verify the inverse, check if $F^{- 1} (F (x)) = x$ and $F (F^{- 1} (x)) = x$ .

Evaluate $F^{- 1} (F (x))$ .

Set up the composite result function.

$F^{- 1} (F (x))$

Evaluate $F^{- 1} (7 x)$ by substituting in the value of $F$ into $F^{- 1}$ .

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

Cancel the common factor of $7$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

$F^{- 1} (7 x) = x$

Evaluate $F (F^{- 1} (x))$ .

Set up the composite result function.

$F (F^{- 1} (x))$

Evaluate $F (\frac{x}{7})$ by substituting in the value of $F^{- 1}$ into $F$ .

$F (\frac{x}{7}) = 7 (\frac{x}{7})$

Cancel the common factor of $7$ .

Cancel the common factor.

$F (\frac{x}{7}) = 7 (\frac{x}{7})$

Rewrite the expression.

$F (\frac{x}{7}) = x$

Since $F^{- 1} (F (x)) = x$ and $F (F^{- 1} (x)) = x$ , then $F^{- 1} (x) = \frac{x}{7}$ is the inverse of $F (x) = 7 x$ .

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

Find the Inverse F(x)=7x

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