Algebra 1 : How to find inverse variation

Study concepts, example questions & explanations for Algebra 1

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Example Questions

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Example Question #1 : How To Find Inverse Variation

Find the inverse of the following function:

 

Possible Answers:

None because the given function is not one-to-one.

Correct answer:

None because the given function is not one-to-one.

Explanation:

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 .

Possible Answers:

Correct answer:

Explanation:

Starting with

Replace with .

We get the following:

Which is equal to .

Example Question #3 : How To Find Inverse Variation

Given:

and

.

Find .

Possible Answers:

Correct answer:

Explanation:

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?

Possible Answers:

Correct answer:

Explanation:

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 =

Possible Answers:

Set F

Set E

Set D

Set B

Set C

Correct answer:

Set C

Explanation:

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 .

Possible Answers:

Correct answer:

Explanation:

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 #6 : How To Find Inverse Variation

 varies inversely as the square root of . If , then . Find  if  (nearest tenth, if applicable).

Possible Answers:

Correct answer:

Explanation:

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 #34 : Basic Single Variable Algebra

 varies inversely as the square of . If , then . Find  if  (nearest tenth, if applicable).

Possible Answers:

Correct answer:

Explanation:

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 #7 : How To Find Inverse Variation

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?

Possible Answers:

Correct answer:

Explanation:

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 #37 : Basic Single Variable Algebra

If  is inversely proportional to  and knowing that  when , determine the proportionality constant.

Possible Answers:

Correct answer:

Explanation:

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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