- #1
EV33
- 196
- 0
Homework Statement
Given f:A→B and g:B→C, let h=g(f(a))
If h is injective, then g is injective.
Give a counter example.
Homework Equations
Injection: Let f:A→B
For all f(x1)=f(x2) implies x1=x2
The Attempt at a Solution
f(a)=[tex]\sqrt{a}[/tex] from [0, infinity]→[0,infinity]
g(b)=b2 from [all real numbers]→[0,infinity]
h(a)=a from [0, infinity]→[0,infinity]
Assuming h is injective and g is not, then this is a counter example. My problem is I am not sure if the square root messes things up here. I know that the square root of a squared is plus or minus a, but because the domain and range can't be negative ( I think), then this works.
So is this correct?