anonymous
  • anonymous
f(x)= 7x+5; g(x)=x^2. Perform function operation of (f+g)(x) and find the domain.
Mathematics
jamiebookeater
  • jamiebookeater
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shadowfiend
  • shadowfiend
First off, remember that \((f+g)(x) = f(x) + g(x)\). So what is \(f(x) + g(x)\) above?
anonymous
  • anonymous
isn't it \[x^{2} +7x+5?\]
shadowfiend
  • shadowfiend
Right-o.

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shadowfiend
  • shadowfiend
Now, what is the `domain' of a function?
anonymous
  • anonymous
i read its the x-value.
shadowfiend
  • shadowfiend
Right. So is there any value of x for which the equation above doesn't give an answer that makes sense?
anonymous
  • anonymous
hmm?
shadowfiend
  • shadowfiend
The range is all real numbers unless there is a value of x for which: \[y = x^2 + 7x + 5\] Gives an undefined y.
shadowfiend
  • shadowfiend
(Hint: for this equation, there is no such value -- all numbers you plug in for x will give you a y value. So, the domain is all real numbers, or \((-\infty, \infty)\).
anonymous
  • anonymous
so its all real numbers? so how do you know when an equation's domain is limited?
shadowfiend
  • shadowfiend
Well, take the equation \(y = \sqrt{x}\).
shadowfiend
  • shadowfiend
If \(x \lt 0\), then the square root is undefined -- it produces an imaginary number. So, the domain of the function is any value >= 0.
anonymous
  • anonymous
i get it you can't have negatives in a square root. so its either a whole number or zero right?
shadowfiend
  • shadowfiend
It's either a *positive* whole number or zero. Negatives are also whole numbers.
anonymous
  • anonymous
okay i get it finally thanks a bunch!! you've been very helpful. :0]
shadowfiend
  • shadowfiend
No problem, glad to help!

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