To find the inverse of the function [tex]\( y = \frac{x}{6} + 12 \)[/tex], you should follow these steps:
1. Start with the given function:
[tex]\[
y = \frac{x}{6} + 12
\][/tex]
2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
This step involves interchanging the roles of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] in the equation to reflect that we are finding the inverse function.
[tex]\[
x = \frac{y}{6} + 12
\][/tex]
3. Solve for [tex]\( y \)[/tex]:
Now, we need to isolate [tex]\( y \)[/tex] on one side of the equation to find the inverse function.
- Subtract 12 from both sides:
[tex]\[
x - 12 = \frac{y}{6}
\][/tex]
The next step is:
4. Multiply both sides by 6 to solve for [tex]\( y \)[/tex]:
[tex]\[
6(x - 12) = y
\][/tex]
So, the inverse function is:
[tex]\[
y = 6x - 72
\][/tex]
Therefore, the next step after swapping [tex]\( x \)[/tex] and [tex]\( y \)[/tex] is:
[tex]\[
x - 12 = \frac{y}{6}
\][/tex]
