Find the Inverse 4/(5+x)

$\frac{4}{5 + x}$

Interchange the variables.

$x = \frac{4}{5 + y}$

Solve for $y$ .

Tap for more steps…

Rewrite the equation as $\frac{4}{5 + y} = x$ .

$\frac{4}{5 + y} = x$

Solve for $y$ .

Tap for more steps…

Multiply each term by $5 + y$ and simplify.

Tap for more steps…

Multiply each term in $\frac{4}{5 + y} = x$ by $5 + y$ .

$\frac{4}{5 + y} \cdot (5 + y) = x \cdot (5 + y)$

Cancel the common factor of $5 + y$ .

Tap for more steps…

Cancel the common factor.

$\frac{4}{5 + y} \cdot (5 + y) = x \cdot (5 + y)$

Rewrite the expression.

$4 = x \cdot (5 + y)$

Simplify $x \cdot (5 + y)$ .

Tap for more steps…

Apply the distributive property.

$4 = x \cdot 5 + x y$

Move $5$ to the left of $x$ .

$4 = 5 x + x y$

Rewrite the equation as $5 x + x y = 4$ .

$5 x + x y = 4$

Subtract $5 x$ from both sides of the equation.

$x y = 4 - 5 x$

Divide each term by $x$ and simplify.

Tap for more steps…

Divide each term in $x y = 4 - 5 x$ by $x$ .

$\frac{x y}{x} = \frac{4}{x} + \frac{- 5 x}{x}$

Cancel the common factor of $x$ .

Tap for more steps…

Cancel the common factor.

$\frac{x y}{x} = \frac{4}{x} + \frac{- 5 x}{x}$

Divide $y$ by $1$ .

$y = \frac{4}{x} + \frac{- 5 x}{x}$

Cancel the common factor of $x$ .

Tap for more steps…

Cancel the common factor.

$y = \frac{4}{x} + \frac{- 5 x}{x}$

Divide $- 5$ by $1$ .

$y = \frac{4}{x} - 5$

Solve for $y$ and replace with $f^{- 1} (x)$ .

Tap for more steps…

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

$f^{- 1} (x) = \frac{4}{x} - 5$

Set up the composite result function.

$g (f (x))$

Evaluate $g (f (x))$ by substituting in the value of $f$ into $g$ .

$g (\frac{4}{5 + x}) = \frac{4}{\frac{4}{5 + x}} - 5$

Simplify each term.

Tap for more steps…

Multiply the numerator by the reciprocal of the denominator.

$g (\frac{4}{5 + x}) = 4 (\frac{5 + x}{4}) - 5$

Cancel the common factor of $4$ .

Tap for more steps…

Cancel the common factor.

$g (\frac{4}{5 + x}) = 4 (\frac{5 + x}{4}) - 5$

Rewrite the expression.

$g (\frac{4}{5 + x}) = 5 + x - 5$

Combine the opposite terms in $5 + x - 5$ .

Tap for more steps…

Subtract $5$ from $5$ .

$g (\frac{4}{5 + x}) = x + 0$

Add $x$ and $0$ .

$g (\frac{4}{5 + x}) = x$

Since $g (f (x)) = x$ , $f^{- 1} (x) = \frac{4}{x} - 5$ is the inverse of $f (x) = \frac{4}{5 + x}$ .

$f^{- 1} (x) = \frac{4}{x} - 5$

Find the Inverse 4/(5+x)

Need help with MATH HOMEWORK