Find the domain of the rational function.

C(x) = x+9/X^2 -16

Domain = {x : x ≠ 4 , -4}  or  (-∞ , -4) ∪ (-4 , 4) ∪ (4 , ∞)

Step-by-step explanation:

TO FIND :-

SOLUTION :-

Domain of a function is a value for which the function is valid.

The function is valid until the denominator is 0.

So make sure that the denominator must not be 0.

Find the values of x for which the denominator becomes 0. To find it , you'll have to solve the above inequality.

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}

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step-by-step explanation: