Question
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Answer
They are not inverses.
Solution
-
We start with the functionIts inverse, denoted
, should satisfy: -
To find the inverse
, let Then, solving for: Interchangingand , we obtain: -
The given function
is: Notice that -
To confirm, we can check the compositions:
-
Compute
: The cube root ofis , but due to the extra , this does not simplify to . -
Compute
: This also does not simplify toin general.
-
-
Since neither composition simplifies to
, the functions and are not inverses of each other.
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The Deep Dive
To determine if
and
are inverses, we need to check if
and
.
Calculating
:
Now, for
:
After calculating it, we find it also simplifies back to
.
Since both compositions return
, Yes, they are inverses!