Question

Which function below is the inverse of f(x) = The quantity of seven x plus one, over two.?

f−1(x) = two over the quantity of seven x plus one

f−1(x) = two over the quantity of one minus seven x

f−1(x) = The quantity of two x plus one, over seven

f−1(x) = The quantity of two x minus one, over seven

Answer 1

Don't worry about the answer choices. Don't need 'em, you just need to know how to find the inverse.

You have:
\[\Large f(x)=\frac{ 7x+1 }{2 }\]

You want to do what is called "switch and solve" method. First, write the function in y=.... notation (instead of f(x)=):

\[\Large y=\frac{ 7x+1 }{2 }\]

Now, the "switch". Anywhere that you have a y, make it an x; and anywhere that you have an x, make it a y:

\[\Large x=\frac{ 7y+1 }{2 }\]

Now, take THAT equation and SOLVE it for y (hence, the "solve" part).

That's your inverse function, \(\Large f^{-1}(x)\)

Answer 2

im confuse, how do i solve for y?

Answer 3

What class is this? if you are in a class where you are finding inverses of function (probably algebra 2?) then you should know how to solve an equation for a specified variable.....

Solve it for y, by isolating the y. Use the properties of equality to "shuffle" the equation around, until you have y=......

Answer 4

i have algebra 2 i just started. i know i have to isolate y but what bout x? is just confusing

Answer 5

I'll get you started: we need to get the y alone, so lets multiply both sides by 2:

\[\Large 2x=\left(\dfrac{ 7y+1 }{2 } \right)\cdot2\]
\[\Large 2x=\left(\dfrac{ 7y+1 }{\cancel 2 } \right)\cdot\cancel 2\]
\[\Large 2x= 7y+1 \]

what's next?

Answer 6

-1 both sides?

Answer 7

I don't understand what you mean, "i know i have to isolate y but what bout x? "

What about x?? Isolate the y on one side, and there will be an x on the other side....

Answer 8

right - good.

Answer 9

and then just one more step

Answer 10

2x - 1 = 7y then divide 7 which would be 7x/7 - 1 = y?

Answer 11

\(\Large 2x-1= 7y\)

Answer 12

Uhm, yes, divide by 7.... but what you get doesn't look like what you have there??

Answer 13

2x*

Answer 14

2x/7 - 1 = y

Answer 15

NO.... not: \(\Large \dfrac{2x}{7}-1= y\)

Look at what you have to do: you need to divide ALL of the LEFT SIDE by 7. Not just the first term.

Answer 16

ohhh my bad my bdad. 2x/7 - 1/7 = y ?

Answer 17

\(\Large \dfrac{1}{7}\cdot(2x-1)= 7y\cdot \dfrac{1}{7}\)

Answer 18

Right! Although I would just put the left side in one rational expression, but what you wrote is equivalent.

\[\Large \dfrac{2x-1}{7}= y\]

Answer 19

thank you very much!

Answer 20

you're welcome. :) happy to help :)

Answer 21

can you help me with this one real quick please?

A function is created to represent the costs of living per person in the family. What restrictions would be made to the domain?

The domain would only include integers.

The domain would only include positive integers.

The domain would only include positive numbers.

The domain would include all real numbers.

Answer 22

The domain is all the values that x (or the independent variable, the "input") is "allowed" to be. Here, the function is cost of living PER PERSON, so I would assume that the x is the number of people in the family.

What KIND of number can that variable be?

Can it be negative? can it be something that's NOT an integer (e.g., 1/2)?

Answer 23

cant be negative and it cant be sumthing thats not an integer. it would be only positive integers? becase there cant be a negative person in the family or half a person in the family?

Answer 24

@DebbieG

Answer 25

Exactly. :)

Answer 26

Which function below is the inverse of f(x) = The quantity of four x minus three, over two. @debbieg

Answer 27

The domain would include all real numbers.
so the last one