Inverse of a fraction?

Question

F(x) = 8/x.
F-1(x) = x/8???

Is that correct and why, or does it remain as 8/x...

because, y= 8/x » x = 8/y » xy = 8 » 8/x?

Answer 1

There are two methods to solve this one:

1. F(x)=y => 8/x=y => xy=8 => x=8/y => F-1(x)=8/x (if you don't understand this, see the chapter on surjectivity)

2. Suppose F-1(x)=a => F(a)=x => 8/a = x => ax=8 => a=8/x => F-1(x)=a

This is based on the property of inverse functions that:
If F(x)=y => F-1(y)=x
which makes sense if you know how to compose functions. If you still can't figure out why, here's the explenation:

F(x)=y
Compose both sides with F-1(x) => F(x)oF-1(x)=F-1(y)
Since F(x)oF-1(x)=x => x=F-1(y)

Hope that helped and you understood everything

Answer 2

it remains 8/x

the work you showed is correct

Answer 3

That's correct - that's just how it is.