Find the Inverse x+19

$x + 19$

Interchange the variables.

$x = y + 19$

Solve for $y$ .

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Rewrite the equation as $y + 19 = x$ .

$y + 19 = x$

Subtract $19$ from both sides of the equation.

$y = x - 19$

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.

$f^{- 1} (x) = x - 19$

Set up the composite result function.

$g (f (x))$

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

$g (x + 19) = (x + 19) - 19$

Combine the opposite terms in $(x + 19) - 19$ .

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Subtract $19$ from $19$ .

$g (x + 19) = x + 0$

Add $x$ and $0$ .

$g (x + 19) = x$

Since $g (f (x)) = x$ , $f^{- 1} (x) = x - 19$ is the inverse of $f (x) = x + 19$ .

$f^{- 1} (x) = x - 19$

Find the Inverse x+19

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