Question
What function is the inverse of the function
A.
, for
B.
, for
C.
, for
D.
, for
B.
C.
D.
Ask by Luna Ellis. in the United States
Jan 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The inverse function is
, for
.
Solution
To find the inverse of the function
, we need to follow these steps:
-
Express the function in terms of
: -
Solve for
: -
Define the inverse function:
Sinceis not one-to-one over all real numbers, we typically restrict the domain to to make it invertible. Thus, the inverse function is:
Looking at the provided options:
- Option B:
, for
This matches our derived inverse function exactly.
Answer:
Option B
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Mind Expander
To find the inverse of the function
, we start by substituting
for
, giving us
. Solving for
involves isolating
on one side, which leads to
. Since we generally restrict
to
for a function to have an inverse, our next step would yield
or simplified,
. Finally, switching
back to
, the inverse function is
for
.
B.
, for
is incorrect since we improperly simplified from the functions given; the principal result lies where we observe
for clearly defined reasons in squaring functions.