Question

hi can u try to help me solve using the domain and function? and show make a graph if possible so I can try understanding.

Answer 1

The domain of a function is the set of input values or values of x that satisfies the function

The expression has an even root. To find the domain, we would exclude values that would make the radicand to be negative. Looking at the expression, the term in the radicand is

x + 3

We would express it as an inequality as shown below

`\begin{gathered} x\text{ + 3 }\ge0 \\ x\text{ }\ge0\text{ - 3} \\ x\text{ }\ge\text{ - 3} \end{gathered}`

From our working, values of x greater than or equal to - 3 would make the value in the square root to be positive. This forms the domain of the function. All numbers lesser than - 3 must be excluded from the domain because they would give a negative value inside the square root. Thus, the domain includes all values greater than - 3

`\text{Domain = x }\ge\text{ - 3}`

The graph of the function is shown below

From the graph, the domain is between the lowest value of x on the left and the highest value of x on the right

We can see that the lowest value of x on the left is - 3

the highest value of x on the right is infinity(all values greater than - 3)