Question

Derivatives of Inverse Functions

Answer 1

I am given a table
x=-2 f(x)=3
x=1 f(x)=2

Answer 2

I have to complete a table of values of x and \[f^{-1}x\]

Answer 3

then I have to figure out \[f^{-1}(f(1))\]

Answer 4

simply swap the columns of first table

Answer 5

ok

Answer 6

if (a, b) is a point on f(x), then (b, a) will be a point on f^(-1)(x)

Answer 7

ok so my answer is 1

Answer 8

Yep !

Answer 9

hmmm w0t?

what I can think offhand is to bear in mind that the f(x)'s DOMAIN is \(f^{-1}\) RANGE and the other way around

Answer 10

thought u have a question about derivatives hmm

Answer 11

I think my worksheet leads into them in a second
ok I got stuck on one of the basic ones

Answer 12

I am also, told x=-2 g(x)=1
x=1 g(x)=-2

Answer 13

okay, this is another problem ?

Answer 14

ahemm \(f(x)\quad \begin{array}{ccllll}
x&y
\\\hline\\
-2&3\\
1&2
\end{array}\qquad
f^{-1}(x)\quad
\begin{array}{llll}
x&y
\\\hline\\
3&2\\
2&1
\end{array}\)

Answer 15

I got stuck on the following

Answer 16

ahemm anyhow -2 \(\large f(x)\quad \begin{array}{ccllll}
x&y
\\\hline\\
-2&3\\
1&2
\end{array}\qquad
f^{-1}(x)\quad
\begin{array}{llll}
x&y
\\\hline\\
3&-2\\
2&1
\end{array}\)

so... see, the functions's DOMAIN is the "inverse"'s RANGE