Question

let f(x)=(absolute val of x)/(x). show that f(x)=1,x>0
f(x)=-1,x<0
find the domain and range of f(x)

Answer 1

domain all numbers except 0

Answer 2

range is 1 and -1

Answer 3

i kind of have to explain how i know that though

Answer 4

\[f(x) = \frac{|x|}{x} = \left\{\begin{array}{rcc}
1 & \text{if} & x >0 \\
-1& \text{if} & x < 0
\end{array}
\right.\]

Answer 5

Well, if x > 0 then |x| = x

Therefore |x|/x = x/x = 1

If x < 0 then |x| = -x

Therefore |x|/x = -x/x = -1

Answer 6

ok well we start with
\[ |x| = \left\{\begin{array}{rcc}
x & \text{if} & x \geq 0 \\
- x& \text{if} & x < 0
\end{array}
\right.\]

Answer 7

that is the definition. then divide by x to get what i wrote above exactly.

Answer 8

what polpak said. hello polpak

Answer 9

Nice latex btw =)

Answer 10

merci. i stole it from zarkon

Answer 11

And I shall steal it from you ;p

Wouldn't have thought to lay that out using an array