inverse; log: find inverse of y = log_2(x - 4), find domain,

The example is::

y=log[sub:12iqdj93]2[/sub:12iqdj93](x-4)

Find the inverse and state the domain and range for the regular function and it's inverse:

what I got wasn't right..

I had the inverse was x= y-4 DIVIDED BY 2.. I got it wrong. help?

The domain and ranges were wrong too.. I put domain of the regular function was All real numbers and the range was y<4
HELP

brittany6990 said:

y=log[sub:14rc7yzi]2[/sub:14rc7yzi](x-4)

Find the inverse and state the domain and range for the regular function and it's inverse:

what I got wasn't right.

Click to expand...

How did you arrive at your answers? (I'm afraid it is not possible to find errors in work that we cannot see. Sorry!)

Please be complete. You started with the original function. To find the inverse, you solved by "x=" by converting the log equation to the equivalent exponential equation, and... then what?

Thank you!

Well I used change of base formula and did

logx-4 divided by log 2

then i did x=logy-4 to start to find the inverse. but idk how to do that from the original equation

Try using the steps provided earlier:

Convert "y = log[sub:14fhxro7]2[/sub:14fhxro7](x - 4)" into the equivalent exponential form, as explained in the logs lesson-link provided earlier, to get 2[sup:14fhxro7]y[/sup:14fhxro7] = x - 4". Then solve for "x=". Then swap the variables, as explained in the inverse-functions lesson-link provided earlier, and rename the new "y" as "f[sup:14fhxro7]-1[/sup:14fhxro7](x)".

:wink:

Hello, brittany6990!

\(\displaystyle f(x)\:=\:\log_2(x-4)\)

Find the inverse.
State the domain and range for the function and it's inverse

Click to expand...

\(\displaystyle \text{We have: }\;\;y \:=\:\log_2(x-4)\)

\(\displaystyle \text{Switch }x\text{ and }y\!:\;\; x \:=\:\log_2(y-4) \quad\Rightarrow\quad \log_2(y-4) \:=\:x\)

\(\displaystyle \text{Solve for }y\!:\;\;y-4 \:=\:2^x \quad\Rightarrow\quad y \;=\;2^x+4\)

. . \(\displaystyle \text{Therefore: }\;\boxed{f^{\text{-}1}(x) \;=\;2^x-4}\)


\(\displaystyle \text{Function}\quad \begin{array}{cc}\text{Domain:} &(4,\:\infty) \\ \text{Range:}& (\text{-}\infty,\:\infty)\end{array}\)

\(\displaystyle \text{Inverse}\quad\begin{array}{cc}\text{Domain:} & (\text{-}\infty,\:\infty) \\ \text{Range:} & (4,\:\infty) \end{array}\)