Question

Use f(x) = 2 x and f-'(x) = 2x to solve the problems.

f(2)=...
F1 (1) =...
F1 (12)) = ...

Answer 1

a) 1

b) 2

c) 2

Explanation:

a)
`f(2)` means find the output for
`(1)/(2)x` when
`x=2`.

`(1)/(2)(2)`

`(2)/(2)`

`1`

b)
`f^(-1)(1)` means find the output for
`2x` when
`x=1`

`2(1)`

`2`

c) If
`f` and
`f^(-1)` are truly inverses then
`f(f^(-1)(u))=u` and
`f^(-1)(f(u))=u` as long as
`u` satisfies the domains.

So we should be able to conclude that
`f^(-1)(f(2))=2` with no work.

However, I will also show work.

`f^(-1)(f(2))`

`f^(-1)(1)` since
`f(2)=1` from part a.

`2` since
`f^(-1)(1)=2` from part b.