Find the Inverse of a Function
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Pre-Calculus › Find the Inverse of a Function
Find the inverse of .
Explanation
To find the inverse of the function, we switch the switch the and
variables in the function.
Switching and
gives
Then, solving for gives our answer:
Find the inverse of the follow function:
Explanation
To find the inverse, substitute all x's for y's and all y's for x's and then solve for y.
Find the inverse function of .
None of the other answers.
Explanation
To find the inverse you must reverse the variables and solve for y.
Reverse the variables:
Solve for y:
Are these two function inverses? and
.
Yes
No
Cannot tell
F(x) does not have an inverse.
G(x) does not have an inverse.
Explanation
One can ascertain if two functions have an inverse by finding the composition of both functions in turn. Each composition should equal x if the functions are indeed inverses of each other.
The functions are inverses of each other.
Determine the inverse function, given
Explanation
In order to find the inverse function we
- switch the variables
and
- solve for the new
variable
For the function
...
Hence, the inverse function is
If , find
.
Explanation
Set , thus
.
Now switch with
.
So now,
.
Simplify to isolate by itself.
So
Therefore,
.
Now substitute with
,
so
, and
.
If , what is its inverse function,
?
Explanation
We begin by taking and changing the
to a
, giving us
.
Next, we switch all of our and
, giving us
.
Finally, we solve for by subtracting
from each side, multiplying each side by
, and dividing each side by
, leaving us with,
.
Find the inverse of this function:
Explanation
In order to have the inverse of a function, the new function must perform the inverse opperations in the opposite order. One way to ensure that is true is to consider the case of , switch x and y, then solve for y.
in this case becomes
.
Our first step in solving is to take the reciprocal power on each side.
The reciprocal of 5 is , so we'll take both sides to the power of 0.2:
Now divide by 2:
Note that the answer has the correct inverse opperations, it is just in the wrong order - first you divide by 2, then you take x to the power of 0.2.
Find the inverse of this function:
Explanation
Write the equation in terms of x and y:
Switch the x and y (this inverts the relationship of the two variables):
Solve for y:
Rewrite to indicate this is the inverse:
Find the inverse of,
.
Explanation
In order to find the inverse, switch the x and y variables in the function then solve for y.
Switching variables we get,
.
Then solving for y to get our final answer.