# How to rank random function from smallest to largest with inverse f included?

1. Sep 5, 2012

### gurpalc

1. The problem statement, all variables and given/known data

The graph of y=f(x) is shown below.

http://newton.science.sfu.ca/cgi-bin/plot.png?file=public_public_1346904771_18810161_plot.data [Broken]
Rank the following from smallest(1) to largest(4).

f−1(0)
f(0)
f(5)
f−1(5)

2. Relevant equations

none available

3. The attempt at a solution

f−1(0) 1
f(0) 3
f(5) 2
f−1(5) 4

Because if f(0) is 4, wouldn't that make the co-ordinates (0,4) so inverse would be (4, 0) so inverse f(0) would be 0 no? But I know this is wrong. I don't what I am doing wrong.
Knowing that f(0)= 4 tells you that $f^{-1}(4)= 0$, not $f ^{-1}(0)$. What you need is some x such that f(x)= 0. Where is f(x)= 0 on your graph?