Question

Given F(x) shown below, complete the equation for the inverse of F(x). If necessary, use the slash mark (/) for the division symbol.
F(x)=x-1
f^-1(y)=_______

Answer 1

y/1?

Answer 2

f(x) = x-1

y = x-1 ... replace f(x) with y

x = y -1 ... swap x and y

now solve for y

Answer 3

oh nvm about the swap, they just want you to solve

y = x - 1

for x

Answer 4

okay so its not y/1 its x/1?

Answer 5

Right... weird notation, we saw this on another problem earlier.

Answer 6

You have
y=x-1

What do you do to solve that for x?

Answer 7

you swap the numbers?

Answer 8

I'm not sure what you mean by that. could you be more specific? Or just show the result.

Answer 9

You either add, subtract, multiply or divide, {something} from both sides.

Answer 10

ok you add the -1 and you get y/2

Answer 11

hmmmm.....

if you have

y=x-1

How does adding 1 (which is what you mean: add 1, not add (-1)) to both sides get you y/2 anywhere?

Answer 12

y+??=x-1+??

Answer 13

y/0

Answer 14

well, y/0 would be undefined... but more importantly, I'm puzzled as to how/why you are getting that?

Answer 15

y=x-1
x=y-1
y=x+1

Answer 16

\(y=x-1\)
\(y+1=x-1+1\) add one to both sides
\(y+1=x\) simplify on right side, since -1 +1=0

There is no division involved, but you keep wanting to divide y by stuff. Can you tell me why? I'm just trying to get at where your confusion is coming from.

Answer 17

Well, yes.... that's how I would expect you to find the inverse. However, your teacher appears to want you to NOT swap x & y, but instead just solve the original equation for x. Which is a bit goofy, frankly. I would have done it the way YOU show above, getting

y=x+1

as the inverse for

y=x-1

That's really a notational matter though.

Answer 18

so my final answer is...

Answer 19

final answer is >.