to find the domain, it is usually easier to find values that don't work, and then say, the domain is all values but those values. if we have a fraction, we can't have the denominator being zero, so we say the domain is all values that don't make the denominator zero. for logs, what is being logged has to be greater than zero, so we say the domain is all values such that what is being logged is not less than or equal to zero. for square roots, what is being rooted has to be greater than or equal to zero, so the domain is all values that cause this to happen. of course there are conventions for stating the domain, the two most common ones are the set notation and the interval notation. tell me what values work for the two functions given and i will show you how to state it.
for the range, this is the set of all outputs of a function, so for (a), it would be all u values we can get, and for (b) it would be all g values we can get from plugging in the values of the domain
example. look at the function f(x) = y = x^2. what is the domain and range?
the domain is all x, since we can plug in any x-value and get a y value. so we write,
the range is given by : . why, becuase the graph does not show up for any other y values, we have no output that is negative