Answer:
To summarize:
- The function f(x) = (3x + 2)/(2x - 10) is defined for all real numbers except when the denominator, 2x - 10, is equal to zero.
- Solving 2x - 10 = 0, we find that x cannot be equal to 5, as it would result in a division by zero.
- Any value of x other than 5 lies in the domain of the function f(x).
Explanation:
To determine the values of x that do not lie in the domain of the function f(x) = (3x + 2)/(2x - 10), we need to consider any restrictions or limitations on the x-values.
The function f(x) is defined for all real numbers except for the values that would result in a division by zero.
In this case, the denominator 2x - 10 cannot be equal to zero, as division by zero is undefined.
To find the values of x that make the denominator zero, we can set 2x - 10 equal to zero and solve for x:
2x - 10 = 0
Adding 10 to both sides:
2x = 10
Dividing both sides by 2:
x = 5
Therefore, x cannot be equal to 5, as it would result in a division by zero.
To summarize:
- The function f(x) = (3x + 2)/(2x - 10) is defined for all real numbers except when the denominator, 2x - 10, is equal to zero.
- Solving 2x - 10 = 0, we find that x cannot be equal to 5, as it would result in a division by zero.
- Any value of x other than 5 lies in the domain of the function f(