The domain of the functions are:
- The domain of f(x) = √4x + 6 is [-3/2, ∞) or x >-3/2
- The domain of g(x) = -4√-20x - 6 is (-∞, -3/10] or x < -3/10
- The domain of f(x) = 15 + √5x - 16 is [16/5, ∞) or x >16/5
- The domain of p(x) = √20x + 6 is (-3/10, ∞] or x > -3/10
What are the domains of a function?
The domain of a function is the set of input values the function can take i.e. the set of values the independent variable can assume?
How to determine the domain of the functions?
Function 1
The function is given as:
f(x) = √4x + 6
Set the radicand greater than 0
4x + 6 > 0
Subtract 6 from both sides
4x > -6
Divide by 4
x > -3/2
Express as interval notation
[-3/2, ∞)
Hence, the domain of f(x) = √4x + 6 is [-3/2, ∞) or x >-3/2
Function 2
The function is given as:
g(x) = -4√-20x - 6
Set the radicand greater than 0
-20x - 6 > 0
Add 6 to both sides
-20x > 6
Divide by -20
x < -6/20
Simplify
x < -3/10
Express as interval notation
(-∞, -3/10]
Hence, the domain of g(x) = -4√-20x - 6 is (-∞, -3/10] or x < -3/10
Function 3
The function is given as:
f(x) = 15 + √5x - 16
Set the radicand greater than 0
5x - 16 > 0
Add 16 to both sides
5x > 16
Divide by 5
x > 16/5
Express as interval notation
[16/5, ∞)
Hence, the domain of f(x) = 15 + √5x - 16 is [16/5, ∞) or x >16/5
Function 4
The function is given as:
p(x) = √20x + 6
Set the radicand greater than 0
20x + 6 > 0
Subtract 6 from both sides
20x > -6
Divide by 20
x > -6/20
Simplify
x > -3/10
Express as interval notation
(-3/10, ∞]
Hence, the domain of p(x) = √20x + 6 is (-3/10, ∞] or x > -3/10
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