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Example Questions
Example Question #1 : How To Find Inverse Variation
Find the inverse of the following function:
None because the given function is not one-to-one.
None because the given function is not one-to-one.
which is the same as
If we solve for we get
Taking the square root of both sides gives us the following:
Interchanging and
gives us
Which is not one-to-one and therefore not a function.
Example Question #2 : How To Find Inverse Variation
Given
and
.
Find .
Starting with
Replace with
.
We get the following:
Which is equal to .
Example Question #3 : How To Find Inverse Variation
Given:
and
.
Find .
Start with which is equal to
and then replace with
. We get the following:
which is equal to
Example Question #4 : How To Find Inverse Variation
Which of the following is not a one-to-one function?
Expression 4 is not even a function because for any value of , one gets two values of
violating the definition of a function. If it is not a function, then it can not be an one-to-one function.
Example Question #5 : How To Find Inverse Variation
is a one-to-one function specified in terms of a set of
coordinates:
A =
Which one of the following represents the inverse of the function specified by set A?
B =
C =
D =
E =
F =
Set C
Set F
Set E
Set D
Set B
Set C
The set A is an one-to-one function of the form
One can find by interchanging the
and
coordinates in set A resulting in set C.
Example Question #1 : Indirect Proportionality
varies directly with
, and inversely with the square root of
.
If and
, then
.
Find if
and
.
The variation equation can be written as below. Direct variation will put in the numerator, while inverse variation will put
in the denominator.
is the constant that defines the variation.
To find constant of variation, , substitute the values from the first scenario given in the question.
We can plug this value into our variation equation.
Now we can solve for given the values in the second scenario of the question.
Example Question #2 : Indirect Proportionality
varies inversely as the square root of
. If
, then
. Find
if
(nearest tenth, if applicable).
The variation equation is for some constant of variation
.
Substitute the numbers from the first scenario to find :
The equation is now .
If , then
Example Question #1 : How To Find Inverse Variation
varies inversely as the square of
. If
, then
. Find
if
(nearest tenth, if applicable).
The variation equation is for some constant of variation
.
Substitute the numbers from the first scenario to find :
The equation is now .
If , then
Example Question #31 : Basic Single Variable Algebra
The current, in amperes, that a battery provides an electrical object is inversely proportional to the resistance, in ohms, of the object.
A battery provides 1.2 amperes of current to a flashlight whose resistance is measured at 20 ohms. How much current will the same battery supply to a flashlight whose resistance is measured at 16 ohms?
If is the current and
is the resistance, then we can write the variation equation for some constant of variation
:
or, alternatively,
To find , substitute
:
The equation is . Now substitute
and solve for
:
Example Question #8 : How To Find Inverse Variation
If is inversely proportional to
and knowing that
when
, determine the proportionality constant.
The general formula for inverse proportionality for this problem is
Given that when
, we can find
by plugging them into the formula.
Solve for by multiplying both sides by 5
So .
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