Answer:
The domain by the interval notation is (-∞ , 3)∪(3 , 4)∪(4 , ∞) ⇒ 3rd answer
Explanation:
* Lets revise how to find the domain of the function
- The domain is all values of x that make the expression defined
- To find where the expression is undefined put the denominator
equal 0, to get the values of x which make denominator equal to 0
- The domain will be all the real number except those values
* Now lets solve the problem
∵ f(x) = (x² - 9)/(x² - 7x + 12)
- Let the denominator x² − 7x + 12 equal to 0
∵ x² − 7x + 12 = 0 ⇒ factorize it
- Consider the form x² + bx + c
- Find a pair of integers whose product is c and whose sum is b
- In this case, whose product is 12 and whose sum is −7
- They are -3 and -4
- Write the factored form using these integers.
∴ (x -3)(x - 4) = 0 ⇒ put each bracket = 0
∴ x - 3 = 0 or x - 4 = 0
∵ x - 3 = 0 ⇒ add 3 to both sides
∴ x = 3
∵ x - 4 = 0 ⇒ add 4 to both sides
∴ x = 4
∴ The domain of f(x) is all real number except 3 and 4
* The domain by the interval notation is
(-∞ , 3)∪(3 , 4)∪(4 , ∞)