1.) Please help me find the domain and range of
2.) For f(x) = 4x- and g(x) = (3x+2)^2, please find f(g(x)).
Thanks in advance for your assistance.
Range: It is all real such that the equation has a solution for in the domain. Thus, it means we want to solve, and RHS is always non-negative thus LHS must be non-negative and so we have a constraint that . Square both sides, since a square root exists and so the solution is but we want that . If then which is always true. And similarly with . Thus, the range is .