Let fx square root x and gx x 4 Determine the domain of t

Let f(x) = square root x and g(x) = x - 4. Determine the domain of the composite function and then find the composite function. (g middot f)(x) Domain: Composite function: (g middot f) (x) =

Solution

f(x) = sqrt x ;g(x) = x-4

(g o f)(x) Plug x= f(x) in g(x)

(g o f)(x) = sqrtx -4

Domain : x>=0 [ 0, +inf)

b) g(x) = x-4

(g o g)(x) Plug x= g(x) in g(x)

(g o g)(x) = x-4 -4 = x-8

Domain : ( -inf , +inf)