Question

The next one is a little tricky.
Suppose
f(x) = |x|x
Then
f^{-1}(x)= what? if x\geq0,
and
f^{-1}(x)=what? if x\leq 0.

Answer 1

definition of |x|

\(\large |x| =x \quad x\ge0 \\ \large |x|=-x \quad x\le 0 \)

Answer 2

so what is f(x) when x>= 0 ?

Answer 3

i have no idea

Answer 4

f(x) = |x|x
when x > =0,
|x| = x

so when x>=0
f(x) = x*x = x^2
makes sense ?

Answer 5

yes/no/idk ?

Answer 6

kind of. so when x is less then 0 it is -x^2?

Answer 7

absolutely correct!

Answer 8

okay i think i get it now. thanks again! may have another one for ya haha

Answer 9

welcome ^_^
sure! :)

Answer 10

question on this one still. I can't figure out what the inverse is for the less then 0 one. if f(x)=-x^2 then wouldnt the inverse function be f-1(x)=sqrt(-x)?

Answer 11

y = -x^2
x = -y^2
-x = y^2
\(f^{-1}(x) = \sqrt {-x}\)
yes

Answer 12

thats what i thought but when i plug it in it is wrong.

Answer 13

let me think..

Answer 14

since -x = |x| when x<=0
try
\(f^{-1}(x)=\sqrt{|x|}\)

Answer 15

still wrong :(

Answer 16

:O
i would take a last attempt to this
since x is negative, we take the negative square root
\(f^{-1}(x)= -\sqrt{-x}\)
if thats also incorrect, then even idk whats correct

Answer 17

that was one i tried before, still wrong. :/ thank you though i got the first part of it right!

Answer 18

hmm. sorry
and welcome ^_^