Question

The function g is defined below.

Answer 1

Hello!

The answer is:

The only value of "x" that ARE NOT in the domain of the function g, are -2 and 3.

Restriction: {-2,3}

Why?

Since we are working with a quotient (or division), we must remember that the only restriction for this kind of functions are the values that make the denominator equal to 0, so, the domain of the function will include all the values of "x" that are different than the zeroes or roots of the denominator.

We have the function:

$h(x)=\frac{x-3}{x^2-x-6}$

Where its denominator is :

$x^2-x-6$

Now, finding the roots or zeroes of the expression, by factoring, we have:

We need to find two numbers which product is equal to -6 and its addition is equal to -1, these numbers are -3 and 2, we have:

$-3*2=-6\\-3+2=-1$

So, the factorized form of the expression will be:

$(x-3)*(x+2)$

We have that the expression will be equal to 0 if "x" is equal to "-2" and "3", so, the values that are not in the domain of g are: -2,3.

Hence, we have:

Restriction: {-2,3}

Domain: (-∞,-2)U(-2,3)U(3,∞)

Have a nice day!