Put the steps in order to correctly find the inverse (3 points)

Question

= log3(x+6) - 4 = y

= y= 37+4 - 6

= x= 3y+4 -6

= h-1(x)=log3(x+6)-4

= log3(x+6) =y+ 4

= x+6 = 3y+4

Answer 1

To find the inverse of the function given by the equation \( y = \log_3(x + 6) - 4 \), follow these steps in the correct order:

1. Start with the original equation: \[ = \log_3(x + 6) - 4 = y \]

2. Rewrite the equation to isolate the logarithm: \[ = \log_3(x + 6) = y + 4 \]

3. Convert from logarithmic form to exponential form: \[ = x + 6 = 3^{(y + 4)} \]

4. Solve for \( x \): \[ = x = 3^{(y + 4)} - 6 \]

5. Finally, express the inverse function: \[ = h^{-1}(x) = 3^{(x + 4)} - 6 \]

6. If needed, re-order the terms to correctly reflect the process.

So the correct order of the steps to find the inverse is:

1. \( = \log_3(x + 6) - 4 = y \)
2. \( = \log_3(x + 6) = y + 4 \)
3. \( = x + 6 = 3^{(y + 4)} \)
4. \( = x = 3^{(y + 4)} - 6 \)
5. \( = h^{-1}(x) = 3^{(x + 4)} - 6 \)

Please note that the expressions you provided are slightly confusing due to misrepresentation of notation in some steps (like \( 37 + 4 \) seems incorrect). The final expression of the inverse is corrected to: \[ h^{-1}(x) = 3^{(x + 4)} - 6 \]