Question

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Answer 1

The domain of a(x) is all of R. The domain of b is the range where $x-4 \geq 0, hence \ x \geq 4$. We can calculate the composition boa by changing in the expression for b, every x with a(x). Hence, boa(x)=$\sqrt{(3x+1)-4}$=$\sqrt{3x-3}$. 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$\geq$ 0.Thus, the set where this holds is $3x \geq 3, x \geq 1$. This is also the domain of the function boa(x).