Find the Inverse (3x+2)/4

$\frac{3 x + 2}{4}$

Interchange the variables.

$x = \frac{3 y + 2}{4}$

Solve for $y$ .

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Rewrite the equation as $\frac{3 y + 2}{4} = x$ .

$\frac{3 y + 2}{4} = x$

Multiply both sides of the equation by $4$ .

$3 y + 2 = x \cdot (4)$

Remove parentheses.

$3 y + 2 = x \cdot (4)$

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

$3 y + 2 = 4 x$

Subtract $2$ from both sides of the equation.

$3 y = 4 x - 2$

Divide each term by $3$ and simplify.

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Divide each term in $3 y = 4 x - 2$ by $3$ .

$\frac{3 y}{3} = \frac{4 x}{3} + \frac{- 2}{3}$

Cancel the common factor of $3$ .

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Cancel the common factor.

$\frac{3 y}{3} = \frac{4 x}{3} + \frac{- 2}{3}$

Divide $y$ by $1$ .

$y = \frac{4 x}{3} + \frac{- 2}{3}$

Move the negative in front of the fraction.

$y = \frac{4 x}{3} - \frac{2}{3}$

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

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

$f^{- 1} (x) = \frac{4 x}{3} - \frac{2}{3}$

Set up the composite result function.

$g (f (x))$

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

$g (\frac{3 x + 2}{4}) = \frac{4 (\frac{3 x + 2}{4})}{3} - \frac{2}{3}$

Simplify terms.

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Simplify each term.

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Combine $4$ and $\frac{3 x + 2}{4}$ .

$g (\frac{3 x + 2}{4}) = \frac{\frac{4 (3 x + 2)}{4}}{3} - \frac{2}{3}$

Reduce the expression by cancelling the common factors.

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Reduce the expression $\frac{4 (3 x + 2)}{4}$ by cancelling the common factors.

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Cancel the common factor.

$g (\frac{3 x + 2}{4}) = \frac{\frac{4 (3 x + 2)}{4}}{3} - \frac{2}{3}$

Rewrite the expression.

$g (\frac{3 x + 2}{4}) = \frac{\frac{3 x + 2}{1}}{3} - \frac{2}{3}$

Divide $3 x + 2$ by $1$ .

$g (\frac{3 x + 2}{4}) = \frac{3 x + 2}{3} - \frac{2}{3}$

Combine the numerators over the common denominator.

$g (\frac{3 x + 2}{4}) = \frac{3 x + 2 - 2}{3}$

Simplify the numerator.

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Subtract $2$ from $2$ .

$g (\frac{3 x + 2}{4}) = \frac{3 x + 0}{3}$

Add $3 x$ and $0$ .

$g (\frac{3 x + 2}{4}) = \frac{3 x}{3}$

Cancel the common factor of $3$ .

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Cancel the common factor.

$g (\frac{3 x + 2}{4}) = \frac{3 x}{3}$

Divide $x$ by $1$ .

$g (\frac{3 x + 2}{4}) = x$

Since $g (f (x)) = x$ , $f^{- 1} (x) = \frac{4 x}{3} - \frac{2}{3}$ is the inverse of $f (x) = \frac{3 x + 2}{4}$ .

$f^{- 1} (x) = \frac{4 x}{3} - \frac{2}{3}$

Find the Inverse (3x+2)/4

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