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 x

Question

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

dan815 · Answer

@iambatman

anonymous · Answer

$$f(x) = \log(x+4)-3$$ 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.

anonymous · Answer

So solving for x here, x+4>0 will give you your domain. So what is the domain? :)

anonymous · Answer

4>0?

anonymous · Answer

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?

anonymous · Answer

ohhhhhhhh. Duh. I know how to solve for x but for some reason that did not click for me.

anonymous · Answer

Can you help me set up the second equation as well?

anonymous · Answer

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

anonymous · Answer

ok thank you, i just need help setting up the equation

anonymous · Answer

There is not really a equation for the range, as you can see from the graph, you can produce all the y values

anonymous · Answer

It can be confusing ha, so let me see if I can make it a bit more clear, so you know about exponentials right?

anonymous · Answer

|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)