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Example Questions
Example Question #1 : Find The Inverse Of A Function
Find the inverse of,
.
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.
Example Question #1 : Find The Inverse Of A Function
Find the inverse of,
.
First, switch the variables making into
.
Then solve for y by taking the square root of both sides.
Example Question #3 : Find The Inverse Of A Function
Find the inverse of the following equation.
.
To find the inverse in this case, we need to switch our x and y variables and then solve for y.
Therefore,
becomes,
To solve for y we square both sides to get rid of the sqaure root.
We then subtract 2 from both sides and take the exponenetial of each side, leaving us with the final answer.
Example Question #2 : Find The Inverse Of A Function
Find the inverse of the following function.
To find the inverse of y, or
first switch your variables x and y in the equation.
Second, solve for the variable in the resulting equation.
Simplifying a number with 0 as the power, the inverse is
Example Question #5 : Find The Inverse Of A Function
Find the inverse of the following function.
Does not exist
To find the inverse of y, or
first switch your variables x and y in the equation.
Second, solve for the variable in the resulting equation.
And by setting each side of the equation as powers of base e,
Example Question #3 : Find The Inverse Of A Function
Find the inverse of the function.
To find the inverse we need to switch the variables and then solve for y.
Switching the variables we get the following equation,
.
Now solve for y.
Example Question #4 : Find The Inverse Of A Function
Find the inverse of
So we first replace every with an
and every
with a
.
Our resulting equation is:
Now we simply solve for y.
Subtract 9 from both sides:
Now divide both sides by 10:
The inverse of
is
Example Question #5 : Find The Inverse Of A Function
What is the inverse of
To find the inverse of a function we just switch the places of all and
with eachother.
So
turns into
Now we solve for
Divide both sides by
Example Question #6 : Find The Inverse Of A Function
If , what is its inverse function,
?
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,
.
Example Question #7 : Find The Inverse Of A Function
Find the inverse of .
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:
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