# How do you find the inverse of g( x ) = 6x + 7?

Jun 4, 2017

Answer: $g ' \left(x\right) = \frac{x}{6} - \frac{7}{6}$

#### Explanation:

Find inverse of $g \left(x\right) = 6 x + 7$

To find the inverse of any function, we flip the $x$ and the $y$ in the original function. Here, the $g \left(x\right)$ is functionally a $y$ variable.
So:
$x = 6 y + 7$

Now we solve for $y$ as for a normal function:
$x - 7 = 6 y$

$y = \frac{x}{6} - \frac{7}{6}$

We can write the inverse function using the following notation:
$g ' \left(x\right) = \frac{x}{6} - \frac{7}{6}$