Let fx square root x 4 and gx x2 4 Determine the domain

Let f(x) = square root x - 4 and g(x) = x^2 + 4. Determine the domain of the composite function and then find the composite function. (f middot g)(x) Composite function: (f middot g)(x) =

Solution

f(x) = sqrt( x-4) g(x) = x^2 +4

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

= sqrt ( x^2 -4 +4)

= sqrt(x^2)

= +/- x

Domain : All real ( -inf , +inf)