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

Question

misty1212 · Answer

HI!!

misty1212 · Answer

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 · Answer

range of the log is always $(-\infty, \infty)$

misty1212 · Answer

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

misty1212 · Answer

oops i meant solve 
$$x-1>0$$ in one step

anonymous · Answer

x can be any real number?

misty1212 · Answer

lol i must be tired 
no solve 
$$x+1>0$$ for $x$

anonymous · Answer

Im sorry I'm still a little confused

anonymous · Answer

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 · Answer

you can solve that inequality for $x$ in your head in one step by subtracting $1$ from both sides

anonymous · Answer

that will give you the domain
as @misty1212  said, the range is all real numbers

anonymous · Answer

so x<-1

anonymous · Answer

oh no, not $x<-1$ $$x+1>0\
x>-1$$

anonymous · Answer

ohh opps

anonymous · Answer

so from x>-1, that would be the domain? @misty1212

misty1212 · Answer

yes