and range
find the domain
f(x) =1/√2x+3
Answers
Answer:
Domain is the set of x values in which the function is defined. Range is the set of y values in which the function is defined.
Since we cannot have a negative number under the square-root
2x - 2 ≥ 0
Solve the inequality.
2x ≥ 2
x ≥ 1
The domain is [1, ∞).
To find the range, we simply plug in all the x values into the function that are within the domain. Another thing that is important to know is that as x gets closer to infinity, the value of y gets closer to certain constant but never reaches it. This y value is known as the horizontal asymptote, and serves as an indicator to how low and how high the y values can reach to.
y = √(2(1) - 2) = √0 = 0
y = √(2(2) - 2)) = √2 = 1.414
y = √(2(3) - 2) = √4 = 2
y = √(2(4) - 2) = √6 = 2.449
If we keep going, the value of y increases without any bounds. If you have a graphing calculator, you can easily confirm this.
Range is [0, ∞).
Edwin R.
A thousand thanks Michael!
Report 08/31/15
Michael W.
Edwin, just to add to Michael's answer:
Michael noted that x ≥ 1 was the domain. Yes, x can be equal to 1, because you'd be taking the square root of zero, which is totally legal. In interval notation, however, the (1, ∞) means that 1 is not included in the interval, meaning x > 1, and I don't think that's what you wanted. To show that 1 is included, you'd say [1, ∞), with a square bracket instead of a parenthesis, which says the equivalent of x ≥ 1.
Step-by-step explanation:
plz mark me as brainleist for this ans , becaause i did typeing these words
Answer:
Domain is the set of x values in which the function is defined. Range is the set of y values in which the function is defined.
Since we cannot have a negative number under the square-root
2x - 2 ≥ 0
Solve the inequality.
2x ≥ 2
x ≥ 1
The domain is [1, ∞).
To find the range, we simply plug in all the x values into the function that are within the domain. Another thing that is important to know is that as x gets closer to infinity, the value of y gets closer to certain constant but never reaches it. This y value is known as the horizontal asymptote, and serves as an indicator to how low and how high the y values can reach to.
y = √(2(1) - 2) = √0 = 0
y = √(2(2) - 2)) = √2 = 1.414
y = √(2(3) - 2) = √4 = 2
y = √(2(4) - 2) = √6 = 2.449
If we keep going, the value of y increases without any bounds. If you have a graphing calculator, you can easily confirm this.
Range is [0, ∞).
Edwin R.
A thousand thanks Michael!
Report 08/31/15
Michael W.
Edwin, just to add to Michael's answer:
Michael noted that x ≥ 1 was the domain. Yes, x can be equal to 1, because you'd be taking the square root of zero, which is totally legal. In interval notation, however, the (1, ∞) means that 1 is not included in the interval, meaning x > 1, and I don't think that's what you wanted. To show that 1 is included, you'd say [1, ∞), with a square bracket instead of a parenthesis, which says the equivalent of x ≥ 1.
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