need some help with my h/w, stuck on these problems, please explain the process and how you obtained the answer, thank you!
1. Let f(x)=x^3 - 4 and g(x)= 3rd root of x + 7
-find the composite function (fog)(x) and determine its domaine and range
-Find the composite function (gof)(x) and determine its domain and range
2. Given the function f(x)= 2x+1/x-3
-find the domaine and range of f(x)
-Find the inverse function f^-1(x) and determine its domain and range
-Graph f(x) and f^-1(x)
3. Given the rational function f(x)= x^2+12/x-2
-determine the domain and range of f(x)
-decide whether the function is even, odd, or neither
-find the horizontal and vertical intercepts of f(x)
-list the asymptotes of f(x)
The Attempt at a Solution
First problem I am puzzled by on a few things. I know f o g means plug f(x) into g(x) and solve that way, so 3rd root of (x^3-4+7)=3rd root of (x^3-11) correct? I am confused as to where to go from there.
Then vice versa on that problem with g o f, 3rd root of (x+7) to the 3rd power, the 3's cancel so (x+7-4) so x = -3??
I know domain and range are values on the coordinate plane from which the graph extends to, domain is the x value at which the graph is limited, and range the y value.
The problem is I am unsure of how to find the domain/range, or the correct formula to use to find it.
2. On number 2 I graphed using my calculator and pretty much guessed the domain being (-(infinity), 3) U (3, infinity) Range being (-infinity, -1/3)