Question

Find the f^-1(y) inverse of F(x)
F(x)=x-10

Answer 1

To find the inverse:

Replace f(x) with y
Switch x's and y's, so put x where y is and x where y is.
Solve for y
Replace y with f^-1(x)

Answer 2

so f^-1(x) =x+10

Answer 3

Yup lol

Answer 4

Oh hold on you're finding f^-1(y)

Answer 5

i dont get it?....

Answer 6

So since you're solving for f^-1(y) it's even easier, you're just solving for x, let f(x) = y, so y = x-10 and solve for x.

Answer 7

so whats the answer.

Answer 8

y = x-10 solve for x and then let x = f^-2(y)

Answer 9

f^-1(y)*

Answer 10

your getting me confused you tell me to slove for x so its gonna be x=y-10 all over again.

Answer 11

F(x)=x-10
y=x-10
x=y-10
y=x-10
correct? or wrong
final answer F^-1= 10 +x or why i dont know

Answer 12

Your question is asking for f^-1(y) I gave you steps to solve for f^-1(x), but I told you it's even easier if you need to solve for f^-1(y) since you're given f(x).

I think you don't know what inverse means.

Answer 13

\[f^{-1}(y) \] this means you need a y variable in your final answer.
You're given \[f(x) = x-10 \implies y = x-10\] now just solve for x.
\[x = y+10 \implies f^{-1}(y) = y+10\] because it's a function of y we have to have a y variable or it wouldn't make sense.

Answer 14

ok i get it

Answer 15

So you have the function f(x) which we can say is going towards the right -> and the inverse of f(x) which is f^-1(x) means we go the opposite direction so towards the left <-, that's why we can cancel things out using the inverse.

Answer 16

Yeah, it's sort of messy when you first learn it haha.

Answer 17

what about F(x)=x/6 +3

Answer 18

Are you solving for f^-1(x) or f^-1(y)?

Answer 19

f^-1(y)

Answer 20

So do the same steps as the last question, let f(x) = y and solve for x then let x = f^-1(y).

Answer 21

F(x)=x/6 +3
y=x/6 +3
y-3= x/6
7-3/6=x
so F^-1(y)= y-3/6

Answer 22

Why are you dividing by 6?

Answer 23

To get rid of the 6 on the right side you need to multiply both sides by 6 :p

Answer 24

oh yeah my mistake
so
F^-1(y)=6(y-3)

Answer 25

There we go :)

Answer 26

F(x)=3x+7
F^-1(y)=y-7/3
correct?

Answer 27

Yes, you're dividing by 3 for the whole expression right? f^-1(y) = (y-7)/3