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anonymous

  • 5 years ago

f(x)= 7x+5; g(x)=x^2. Perform function operation of (f+g)(x) and find the domain.

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  1. shadowfiend
    • 5 years ago
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    First off, remember that \((f+g)(x) = f(x) + g(x)\). So what is \(f(x) + g(x)\) above?

  2. anonymous
    • 5 years ago
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    isn't it \[x^{2} +7x+5?\]

  3. shadowfiend
    • 5 years ago
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    Right-o.

  4. shadowfiend
    • 5 years ago
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    Now, what is the `domain' of a function?

  5. anonymous
    • 5 years ago
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    i read its the x-value.

  6. shadowfiend
    • 5 years ago
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    Right. So is there any value of x for which the equation above doesn't give an answer that makes sense?

  7. anonymous
    • 5 years ago
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    hmm?

  8. shadowfiend
    • 5 years ago
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    The range is all real numbers unless there is a value of x for which: \[y = x^2 + 7x + 5\] Gives an undefined y.

  9. shadowfiend
    • 5 years ago
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    (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 \((-\infty, \infty)\).

  10. anonymous
    • 5 years ago
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    so its all real numbers? so how do you know when an equation's domain is limited?

  11. shadowfiend
    • 5 years ago
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    Well, take the equation \(y = \sqrt{x}\).

  12. shadowfiend
    • 5 years ago
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    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.

  13. anonymous
    • 5 years ago
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    i get it you can't have negatives in a square root. so its either a whole number or zero right?

  14. shadowfiend
    • 5 years ago
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    It's either a *positive* whole number or zero. Negatives are also whole numbers.

  15. anonymous
    • 5 years ago
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    okay i get it finally thanks a bunch!! you've been very helpful. :0]

  16. shadowfiend
    • 5 years ago
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    No problem, glad to help!

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