Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

F(g(x)) problem, about the domain.

  1. Oct 10, 2006 #1
    Ok, f(x)=x^2 g(x)=sq.rt.(2-x)

    Problem: f(g(x))

    You end up with the answer 2-x but how come you need a domain for the answer? How come the domain is (-infinity,2]????
  2. jcsd
  3. Oct 10, 2006 #2
    Because while your answer simplifies to 2-x, you have to remember that there's a sqrt(2-x) in there... you can't take the square root of a negative number.

    Here's an example: [tex]f(x)=\frac{x^2+3x+2}{x+2} = \frac{(x+2)(x+1)}{x+2}[/tex]

    While it's obvious that the expression simplifies, you have to remember that you can't divide by zero. Thus, the value of -2 for x is not allowed in the original function. If you simplify the function, it becomes x+1, x doesn't equal 2.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook