The domain of a(x) is all of R. The domain of b is the range where [tex]x-4 \geq 0, hence \ x \geq 4[/tex]. We can calculate the composition boa by changing in the expression for b, every x with a(x). Hence, boa(x)=[tex] \sqrt{(3x+1)-4} [/tex]=[tex] \sqrt{3x-3} [/tex]. Again for a function with a root to be defined, we need that the expression under the square root has to be positive. Hence, 3x-3[tex] \geq [/tex] 0.Thus, the set where this holds is [tex]3x \geq 3, x \geq 1[/tex]. This is also the domain of the function boa(x).
