What is the domain of f(x) = log(x + 4) - 2?
x > -4
x ≥ -4
x > 4
All Real Numbers
What is the range of f(x) = log(x)?
All Real Numbers
y > 0
y < 0
y ≥ 0
What is the domain of f(x) = log(x) - 1?
All Real Numbers
x ≥ 0
x > 0
x < 0
Stacey Warren - Expert brainly.com
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\[f(x) = \log(x+4)-3\] to find the domain set it up \[x+4>0\] essentially when we deal with logarithms the domain of y = logx, we have x>0 for the domain.
So solving for x here, x+4>0 will give you your domain. So what is the domain? :)
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Hmm, not quite, all you have to do is subtract 4 from both sides, don't let the > worry you. You can solve it the same way as if it were a equal sign (=) except if we were multiplying or dividing by a negative the sign would flip, but for now just ignore that.
x+4>0 so if we subtract -4 from both sides, we would get x>-4 right?
ohhhhhhhh. Duh. I know how to solve for x but for some reason that did not click for me.
Can you help me set up the second equation as well?
So notice that domain is what the x can be and range is what the y can be. When we deal with range for a logarithmic function, it is usually always all real numbers.|dw:1439851927862:dw| this is the graph of the function
ok thank you, i just need help setting up the equation
There is not really a equation for the range, as you can see from the graph, you can produce all the y values
It can be confusing ha, so let me see if I can make it a bit more clear, so you know about exponentials right?
|dw:1439852429416:dw| Here the \[y=2^x\] is an exponential function. The inverse of this function is\[x=2^y\], and is a logarithmic function. You can probably see here that these are mirrors of each other, with the axis of symmetry being the diagonal line of y = x.
Since these are inverses of each other we can express the same information in different ways looking at the same conditions. (Bear with me here, this is what shows us the domain and range)
Again notice \[y=2^x\] is exponential and you can see that the domain is all real numbers and the range obviously being y>0 and see that \[x=2^y\] the logarithmic function the domain is x>0 and the range is all real numbers, so here is why we can say range is usually always all real numbers for logarithmic functions, does that help?
For the last question it's the same as we did before, as I mentioned earlier \[f(x) = logx\] we have x>0, so that's it for that one haha.