For this written assignment, answer the following questions showing all of your work.
1. Find the domain of the function using interval notation.
f (x) = √𝑥 − 6
√𝑥 − 4
When dealing with square root functions, we need to remember that
√0 = 0 √𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 = valid output
√𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 = invalid
√𝑥 − 6 is valid only when x - 6 ≥ 0
x≥6
√𝑥 − 4 is valid only when x - 4 > 0
(Here x – 4 ≠ 0, as it is the denominator of the fraction)
x>4
Using the line graph
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
The common portion of these solutions set given by (4,∞) ∩ [6,∞)
= [6,∞) is the domain of f(x).
1. Find the domain of the function using interval notation.
f (x) = √𝑥 − 6
√𝑥 − 4
When dealing with square root functions, we need to remember that
√0 = 0 √𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 = valid output
√𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 = invalid
√𝑥 − 6 is valid only when x - 6 ≥ 0
x≥6
√𝑥 − 4 is valid only when x - 4 > 0
(Here x – 4 ≠ 0, as it is the denominator of the fraction)
x>4
Using the line graph
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
The common portion of these solutions set given by (4,∞) ∩ [6,∞)
= [6,∞) is the domain of f(x).
