Question

given f(x) shown below, complete the equation for the inverse of f(x). if necessary use the slash mark (/) for the division problem
f(x)=3x+6
F^-1(y)=_____

Answer 1

i really need help

Answer 2

To find the inverse all you need to do is switch y and x around.

Answer 3

yes i know that but i forgot because people were telling me different things and i got all of my ?s wronggg

Answer 4

Well inverse is just switching. So f(x)=3x+6 becomes x=3y+6
Now just solve for y

Answer 5

-6 to both sides right

Answer 6

Yup

Answer 7

y=1/3?

Answer 8

x=3y+6

Subtracting 6 from both sides should give you
x-6=3y

Then solve for y. You will get y as an expression of x, a FUNCTION, not a NUMBER.

Answer 9

\[f ^{-1}(y)=\frac{ 1 }{ 3 }\]

Answer 10

But @romanortiz65 , as some of us were telling you yesterday, your teacher's notation is very weird because in your question you have:
F^-1(y)=

Usually when you find an inverse, you give it in terms of x, not in terms of y. So the way that @Luigi0210 described above is absolutely the standard approach to this type of problem (switch x and y in the original function and then solve that expression for y), but your teacher asking for the function to be in terms of y, which you would get if you DON'T switch the variables and simply solve the original equation for x.

Answer 11

\[f ^{-1}(y)=\]

Answer 12

You have \[\large x=3y+6\] you subtract 6 from each side and get \[\large x-6=3y\]
How are you getting from that, to \(y=\dfrac{1}{3}\)??

Answer 13

it should be written as this

Answer 14

ohhhhh i see

Answer 15

\[\frac{ x-6 }{ 3 }\]

Answer 16

is the answer

Answer 17

Yes, after you solve the equation for y as a function of x, you TYPICALLY write \[y=f ^{-1}(x)\]

This is the oddity of the notation that you are being asked for, since you are giving a function of y it would be \[x=f ^{-1}(y)\] and I'm not sure what to make of that, lol.

Answer 18

Yes, (x-6)/3 is correct.

Answer 19

ok no wonder i got all my test wrong i kept on writting them as x-6/3