I like the work you have done here. It might be useful to know that
the domain of is the range of and
the range of is the domain of
To make your square roots look better use \sqrt{} instead of \sqrt()
This is the difference between and
the questino is
A)find domain and range
b)find domain and range of inverse function
c)Find an explicit formula for the inverse function as a function of x.
a)domain of original function is [4, infinity)
How do I find the range?
b)domain of inverse function is range of original function, range of inverse function is domain of original function so [4, infinity)
c) the formula for the inverse function is
i would think that the range would be [9, infinity), since 9 would be the lowest number than can still make the square root non negative, but the book's answer says the range of the original function/domain of inverse is [-5, infinity) does this have something to do with the restricted domain? if so, what do I do to get this range?
[HTML][/HTML] The point of using "4" is that your domain is .
Another important point is that is equal to -9 when x= 2 and is larger than -9 for all other x, because is positive for all x except 2. That is, the graph is a parabola with vertex at (2, 9). But your domain is - what does the parabola look like past x= 4? What does that tell you about the domain?
Now, as for the inverse, a standard way of finding inverse functions is to "swap" x and y: if y= f(x) then . From you get . Solve for y. When taking the square root, to 'invert' the square, remember that y must be larger than or equal to 4.