anonymous
  • anonymous
Graph the function g(x)=-3+log4(x+1) and give its domain and range using interval notation.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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misty1212
  • misty1212
HI!!
misty1212
  • misty1212
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
misty1212
  • misty1212
range of the log is always \((-\infty, \infty)\)

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misty1212
  • misty1212
and you can't take the log of a negative number, so to find the domain, solve \[x-1>0\) in one step
misty1212
  • misty1212
oops i meant solve \[x-1>0\] in one step
anonymous
  • anonymous
x can be any real number?
misty1212
  • misty1212
lol i must be tired no solve \[x+1>0\] for \(x\)
anonymous
  • anonymous
Im sorry I'm still a little confused
anonymous
  • anonymous
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
anonymous
  • anonymous
you can solve that inequality for \(x\) in your head in one step by subtracting \(1\) from both sides
anonymous
  • anonymous
that will give you the domain as @misty1212 said, the range is all real numbers
anonymous
  • anonymous
so x<-1
anonymous
  • anonymous
oh no, not \(x<-1\) \[x+1>0\\ x>-1\]
anonymous
  • anonymous
ohh opps
anonymous
  • anonymous
so from x>-1, that would be the domain? @misty1212
misty1212
  • misty1212
yes

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