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anonymous

  • one year ago

Graph the function g(x)=-3+log4(x+1) and give its domain and range using interval notation.

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  1. misty1212
    • one year ago
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    HI!!

  2. misty1212
    • one year ago
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    here is a nice picture, but make sure to click on "real valued plot" so as not to get confused with complex numbers http://www.wolframalpha.com/input/?i=-3%2Blog_4%28x-1%29

  3. misty1212
    • one year ago
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    range of the log is always \((-\infty, \infty)\)

  4. misty1212
    • one year ago
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    and you can't take the log of a negative number, so to find the domain, solve \[x-1>0\) in one step

  5. misty1212
    • one year ago
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    oops i meant solve \[x-1>0\] in one step

  6. anonymous
    • one year ago
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    x can be any real number?

  7. misty1212
    • one year ago
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    lol i must be tired no solve \[x+1>0\] for \(x\)

  8. anonymous
    • one year ago
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    Im sorry I'm still a little confused

  9. anonymous
    • one year ago
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    the input in the log must be positive your input is \(x+1\) so \(x+1\) has to be positive, i.e. \(x+1>0\) is what you know first

  10. anonymous
    • one year ago
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    you can solve that inequality for \(x\) in your head in one step by subtracting \(1\) from both sides

  11. anonymous
    • one year ago
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    that will give you the domain as @misty1212 said, the range is all real numbers

  12. anonymous
    • one year ago
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    so x<-1

  13. anonymous
    • one year ago
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    oh no, not \(x<-1\) \[x+1>0\\ x>-1\]

  14. anonymous
    • one year ago
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    ohh opps

  15. anonymous
    • one year ago
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    so from x>-1, that would be the domain? @misty1212

  16. misty1212
    • one year ago
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    yes

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