Question

For the real-valued functions g(x)=4x-1 and h(x)=sqrt(x-3), find the composition g o h (g of h) and specify its domain using interval notation

Answer 1

g o h = g of h = g(h(x)) = g(sqrt(x - 3)) = 4sqrt(x - 3) - 1. The domain restrictions of the composition function is like an intersection (or an inclusion, maybe) of the parts. The only function that has such restrictions in this case is h. [3, infinity) is its domain. This is also the domain of g o h.

Answer 2

Thank you