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ChatGPT
Aug 10
To find the domain and range of the function g(x) = √(4 - 7x), we need to consider the restrictions on the input values (x) and the output values (g(x)).
Domain:
The domain of a square root function is the set of all real numbers that make the radicand (the expression inside the square root) non-negative. In this case, the radicand is 4 - 7x. To find the domain, we need to solve the inequality 4 - 7x ≥ 0:
4 - 7x ≥ 0
7x ≤ 4
x ≤ 4/7
Therefore, the domain of g(x) is all real numbers less than or equal to 4/7, or (-∞, 4/7].
Range:
The range of a square root function is the set of all real numbers that the function can output. Since the square root of a non-negative number is always non-negative, the range of g(x) = √(4 - 7x) is all non-negative real numbers.
Therefore, the range of g(x) is [0, ∞).
Domain:
The domain of a square root function is the set of all real numbers that make the radicand (the expression inside the square root) non-negative. In this case, the radicand is 4 - 7x. To find the domain, we need to solve the inequality 4 - 7x ≥ 0:
4 - 7x ≥ 0
7x ≤ 4
x ≤ 4/7
Therefore, the domain of g(x) is all real numbers less than or equal to 4/7, or (-∞, 4/7].
Range:
The range of a square root function is the set of all real numbers that the function can output. Since the square root of a non-negative number is always non-negative, the range of g(x) = √(4 - 7x) is all non-negative real numbers.
Therefore, the range of g(x) is [0, ∞).
0
Google Gemini AI
Aug 10
Domain:
The domain of a function is the set of all possible input values that make the function defined. Since the square root function is only defined for non-negative numbers, we have:
```
4 - 7x ≥ 0
```
Solving for x:
```
-7x ≥ -4
x ≤ 4/7
```
Therefore, the domain of g(x) is (-∞, 4/7]
Range:
The range of a function is the set of all possible output values that the function can produce. Since the square root function can only produce non-negative outputs, we have:
```
0 ≤ root 4 - 7x < ∞
```
Therefore, the range of g(x) is [0, ∞)
The domain of a function is the set of all possible input values that make the function defined. Since the square root function is only defined for non-negative numbers, we have:
```
4 - 7x ≥ 0
```
Solving for x:
```
-7x ≥ -4
x ≤ 4/7
```
Therefore, the domain of g(x) is (-∞, 4/7]
Range:
The range of a function is the set of all possible output values that the function can produce. Since the square root function can only produce non-negative outputs, we have:
```
0 ≤ root 4 - 7x < ∞
```
Therefore, the range of g(x) is [0, ∞)
0
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Aug 10
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