Question
The set {x:x∈R,x≠27} is the domain of which of the following functions?(1 point) Responses t(x)=12x+7 t times x is equal to the fraction with numerator 1 and denominator 2 x plus 7 t(x)=17x−2 t times x is equal to the fraction with numerator 1 and denominator 7 x minus 2 t(x)=12x−7 t times x is equal to the fraction with numerator 1 and denominator 2 x minus 7 t(x)=17x+2 t times x is equal to the fraction with numerator 1 and denominator 7 x plus 2
Answers
Answer
wrong
Answered by
GPT-4o mini
To determine which function has the domain {x: x ∈ R, x ≠ 27}, we need to identify any potential restrictions on the function based on its formulation. A common reason for a restriction in the domain is the presence of denominators that can result in division by zero.
Let's consider each option:
1. **\( t(x) = 12x + 7 \)**
- This function is a linear function and has no restrictions on the domain. The domain is all real numbers, \( \mathbb{R} \).
2. **\( t(x) = \frac{1}{2x + 7} \)**
- Here, we need to consider when the denominator is zero:
\[ 2x + 7 = 0 \]
\[ x = -\frac{7}{2} \]
- The domain would be all real numbers except \( -\frac{7}{2} \).
3. **\( t(x) = 17x - 2 \)**
- This is also a linear function with no restrictions on the domain. The domain is all real numbers, \( \mathbb{R} \).
4. **\( t(x) = \frac{1}{7x - 2} \)**
- For this function, we check the denominator:
\[ 7x - 2 = 0 \]
\[ x = \frac{2}{7} \]
- The domain is all real numbers except \( \frac{2}{7} \).
5. **\( t(x) = 12x - 7 \)**
- This is another linear function with no restrictions on the domain. The domain is \( \mathbb{R} \).
6. **\( t(x) = \frac{1}{2x - 7} \)**
- Checking the denominator:
\[ 2x - 7 = 0 \]
\[ x = \frac{7}{2} \]
- The domain is all real numbers except \( \frac{7}{2} \).
7. **\( t(x) = 17x + 2 \)**
- This is also a linear function with no restrictions. The domain is \( \mathbb{R} \).
8. **\( t(x) = \frac{1}{7x + 2} \)**
- Checking the denominator:
\[ 7x + 2 = 0 \]
\[ x = -\frac{2}{7} \]
- The domain is all real numbers except \( -\frac{2}{7} \).
None of the given functions clearly have \( x = 27 \) as a restriction in their domains.
Therefore, the **correct answer** is:
- None of these functions specifically has the domain {x: x ∈ R, x ≠ 27}.
Let's consider each option:
1. **\( t(x) = 12x + 7 \)**
- This function is a linear function and has no restrictions on the domain. The domain is all real numbers, \( \mathbb{R} \).
2. **\( t(x) = \frac{1}{2x + 7} \)**
- Here, we need to consider when the denominator is zero:
\[ 2x + 7 = 0 \]
\[ x = -\frac{7}{2} \]
- The domain would be all real numbers except \( -\frac{7}{2} \).
3. **\( t(x) = 17x - 2 \)**
- This is also a linear function with no restrictions on the domain. The domain is all real numbers, \( \mathbb{R} \).
4. **\( t(x) = \frac{1}{7x - 2} \)**
- For this function, we check the denominator:
\[ 7x - 2 = 0 \]
\[ x = \frac{2}{7} \]
- The domain is all real numbers except \( \frac{2}{7} \).
5. **\( t(x) = 12x - 7 \)**
- This is another linear function with no restrictions on the domain. The domain is \( \mathbb{R} \).
6. **\( t(x) = \frac{1}{2x - 7} \)**
- Checking the denominator:
\[ 2x - 7 = 0 \]
\[ x = \frac{7}{2} \]
- The domain is all real numbers except \( \frac{7}{2} \).
7. **\( t(x) = 17x + 2 \)**
- This is also a linear function with no restrictions. The domain is \( \mathbb{R} \).
8. **\( t(x) = \frac{1}{7x + 2} \)**
- Checking the denominator:
\[ 7x + 2 = 0 \]
\[ x = -\frac{2}{7} \]
- The domain is all real numbers except \( -\frac{2}{7} \).
None of the given functions clearly have \( x = 27 \) as a restriction in their domains.
Therefore, the **correct answer** is:
- None of these functions specifically has the domain {x: x ∈ R, x ≠ 27}.
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