Question

Find the domain:

y= (6+9x)/(6−|x−1|)

Answer 1

The domain = {x : x ≠ -5 , 7}

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
`y=(6+9x)/((6-Ix-1I))`

- 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}