Basic Function Concepts 199
Solution
a. x= 4
Step 1. Check whether 4 is in the domain of the function.
The square root of a negative number is not a real number, so set
x − 3 ≥ 0 and solve the inequality to determine the domain of the
function.
x− 30 ≥
x≥ 3
The domain is all real numbers greater than or equal to 3. Thus, 4 is
in the domain of g.Step 2. Substitute 4 for x in the equation and evaluate.g() 4 44 − (^32) () 4
g() 4 11 + 8
g()) 9
b. x= 1
Step 1. Check whether 1 is in the domain of the function.
The square root of a negative number is not a real number, so set
x− 30 ≥ and solve the inequality to determine the domain of the
function.
x− 30 ≥
x≥ 3
The domain is all real numbers greater than or equal to 3. Thus, 1 is
not in the domain of g, so the function has no value at 1.
c. x= 8
Step 1. Check whether 8 is in the domain of the function.
The square root of a negative number is not a real number, so set
x− 30 ≥ and solve the inequality to determine the domain of the
function.
x− 30 ≥
x≥ 3
The domain is all real numbers greater than or equal to 3. Thus, 8 is
in the domain of g.