Question
If a function
, what is its inverse function?
Ask by King Hart. in the United States
Dec 28,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The inverse function of
is
.
Solution

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The Deep Dive
To find the inverse function, start by replacing
with
:
. Now, swap
and
, giving you
. Then, solve for
: subtract 2 from both sides, resulting in
, and finally divide by 3:
. So the inverse function is
.
Interestingly, inverse functions can often be visualized as reflections over the line
. If you graph
and its inverse
, you’ll see that they create a perfect mirror image along that line. This demonstrates how every input-output pair in one function corresponds to an output-input pair in its inverse!