Question

g(x) = |x| Is that a one-one function? Why?

Answer 1

In a 1<-->1 function, for every x, there is a unique y. And, for every y, there is a unique x.

In g(x) = |x|, 1 is mapped to 1 and -1 is also mapped to 1.
On the flip side, a y of 1 is mapped to x values both 1 and -1.

Answer 2

so since -1 and 1 both become 1 that means it isnt a 1-1 function?

Answer 3

Yes, both of these conditions are required:

In g(x) = |x|, 1 is mapped to 1 and -1 is also mapped to 1.
On the flip side, a y of 1 is mapped to x values both 1 and -1.

One-to-One Function

A function for which every element of the range of the function corresponds to exactly one element of the domain. One-to-one is often written 1-1.

Note: y = f(x) is a function if it passes the vertical line test. It is a 1-1 function if it passes both the vertical line test and the horizontal line test.

http://www.mathwords.com/o/one_to_one_function.htm

Answer 4

many thanks man!