Question

Identify the domain for the function !!! 10 points. Help needed!!

Answer 1

Hello!

The answer is:

The domain for the function is:

Domain:(-∞,-3)∪(-3,∞)

Why?

Since we are working with fractions, the only restriction that we will have for the function is when the denominator of the function tends to 0.

We are given the function:

$f(x)=\frac{x^3} +27}{x+3}$

We have two expressions:

The first expression (numerator) has no restriction, however, we can find a restriction at the second expression (denominator) because when a fraction has a denominator equal to 0, the function does not exist on the real numbers.

For the denominator, we have that it tends to 0 at:

$x=-3$

So, the domain for the given function will be:

Domain:(-∞,-3)∪(-3,∞)

Hence, the answer is the second option, the domain for the function is:

Domain:(-∞,-3)∪(-3,∞)

Have a nice day!