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Question 452404: Find the domain of the function and express the answer in interval not action explain in words..
A) f (x) = 4x^2 - 7x +3
B. g (x) = 10/x+7
C. f (x) = ^ 4x-16 ( this is over the sign that looks like a check mark
d. g (x) = 2x/x-3
e. f (x) = 3x-9
Explain in words and show all work..
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find the domain of the function and express the answer in interval not action explain in words..
A) f (x) = 4x^2 - 7x +3
B. g (x) = 10/x+7
C. f (x) = ^ 4x-16 ( this is over the sign that looks like a check mark
d. g (x) = 2x/x-3
e. f (x) = 3x-9
Explain in words and show all work.
..
When checking for domain, you are looking for restrictions, that is, x-values which makes f(x) invalid or undefined.
..
A) f (x) = 4x^2 - 7x +3
Does not appear to be any restrictions.
In words: all real numbers
Interval Notation: (-∞,∞)
..
B. g (x) = 10/x+7
The restriction is in the denominator which cannot be zero. If the denominator=0, f(x) becomes undefined.
Domain:
In words: all real numbers except when x+7=0 or x=-7
Interval Notation: (-∞,-7) U (-7,∞)
..
C. f (x) = ^ 4x-16 ( this is over the sign that looks like a check mark
The check mark you mentioned I believe is the sqrt symbol like √, So, what you have here is:
sqrt(4x-16)
For a sqrt expression to be valid, what is inside must be ≥ 0.
So, 4x-16≥0
4x≥16
x≥4
Domain:
In words: All real numbers equal to or greater than 4
Interval Notation: [4,∞)
..
d. g (x) = 2x/x-3
Restriction in denominator
Domain:
In words: all real numbers except when x-3=0 or x=3
Interval Notation: (-∞,3) U (3,∞)
..
e. f (x) = 3x-9
No restrictions
Domain:
In words: all real numbers
Interval Notation: (-∞,∞)
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