Pregunta
The function
is a translation of the parent cubic function. What is the
inverse? (1 point)
inverse? (1 point)
Ask by Stanley Hilton. in the United States
Jan 23,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The inverse function is
.
Solución

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Como
Extra Insights
To find the inverse of the function
, we first rewrite the equation by replacing
with
:
Next, we solve for
in terms of
:
- Subtract 4 from both sides:
- Take the cube root of both sides:
Now swapping
and
gives us the inverse function:
So, the correct choice is
.
Now, let’s have some fun with this!
Did you know that the parent cubic function
has a “S” shape and is actually symmetric about the origin? When we add 4 to it, we effectively lift this function up 4 units, transforming our visually engaging cubic curve. This means the roots (where
) shift as well, an important aspect in understanding function transformations!
When working with inverses, a common mistake is not accurately swapping
and
before solving for the inverse. Remember, the inverse function essentially “undoes” the original function. To verify your work, always check by plugging the inverse back into the original function to see if you get
back — it should be a satisfying roundtrip!
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