Answer:
Domain = {x : x ≠ 4 , -4} or (-∞ , -4) ∪ (-4 , 4) ∪ (4 , ∞)
Step-by-step explanation:
TO FIND :-
- Domain of [tex]C(x) = \frac{x + 9}{x^2 - 16}[/tex]
SOLUTION :-
Domain of a function is a value for which the function is valid.
The function [tex]C(x) = \frac{x + 9}{x^2 - 16}[/tex] is valid until the denominator is 0.
So make sure that the denominator must not be 0.
[tex]=> x^2 - 16 > 0[/tex]
Find the values of x for which the denominator becomes 0. To find it , you'll have to solve the above inequality.
[tex]=>x^2 - 16 + 16 > 0 + 16[/tex]
[tex]=> x^2 > 16[/tex]
[tex]=> x > \sqrt{16}[/tex]
[tex]=> \boxed{x > 4} \: or \:\boxed{x > -4}[/tex]
We can say that 4 & -4 can't be domains because these values will make the function undefined.
Now try putting values of x such that -4 < x < 4. You'll observe that the function will be valid for all those values of x between -4 & 4.
CONCLUSION :-
The function will be valid for any value of 'x' except 4 & -4. So in :-
Interval notation , it can be written as → (-∞ , -4) ∪ (-4 , 4) ∪ (4 , ∞)
Set builder notation , it can be written as → {x : x ≠ 4 , -4}
