Answer:
The domain = {x : x ≠ -5 , 7}
Step-by-step explanation:
- The domain of the function is the values of x which makes the function
defined
- If the function has a denominator then the domain is all the values of x
except the zeroes of the denominator
- Zeroes of the denominator means the values of x when the
denominator = 0
- The function is [tex]y=\frac{6+9x}{(6-Ix-1I)}[/tex]
- To find the domain of the function find the zeroes of the denominator
∵ The denominator is ⇒ 6 - Ix - 1I
∴ 6 - Ix - 1I = 0
- Subtract 6 from both sides
∴ - Ix - 1I = -6
- Multiply both sides by -1
∴ Ix - 1I = 6
- The absolute value of x - 1 = 6 that means x - 1 = 6 OR x - 1 = -6
∵ x - 1 = 6
- Add 1 to both sides
∴ x = 7
∵ x - 1 = -6
- Add 1 to both sides
∴ x = -5
∴ The zeroes of the denominator are -5 and 7
∵ x = -5 and x = 7 make the denominator = 0
- Any value divided by 0 is undefined
∴ x can be any value except -5 and 7
∴ The domain of the function is all real values of x except -5 and 7
* The domain = {x : x ≠ -5 , 7}
