1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Domain and range can't be negative

  1. Jul 31, 2010 #1
    1. The problem statement, all variables and given/known data
    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.

    2. Relevant equations
    Injection: Let f:A→B

    For all f(x1)=f(x2) implies x1=x2

    3. 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?
  2. jcsd
  3. Jul 31, 2010 #2
    Re: Injection

    I believe you are correct.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook