The function is defined below. h(x)=x-6/x^2-81

Question

The function g is defined below. g(x)=(x^2)(-12x+35)/(x-5)

Find all values of
that are NOT in the domain of .
If there is more than one value, separate them with
commas.

Answer 1

for h(x)=(x-6)/(x²-81), any number devided by zero is undefined.

So equating you denominator to "0" and solve for x will gives values not in the domain.

→x²-81= x²-9²=0  (difference of squares)

→(x-9)(x+9)=0

→x-9=0 and x+9=0

→x=9 and x=-9 not in the domain.

For the second question.

Again, the denominator is,  x-5

→x-5=0

→x=5 is not in the domain.

Answer 2

If I understand correctly, you are looking for values of x that are not in the domain of the function:

g(x)=(x^2)(-12x+35)/(x-5)

The key to finding values that are not in the domain of the function is finding any values that produce 0 in the denominator or negative numbers under radicals that have an even index (like a square root).

Since the function is a fraction, the domain of the function excludes any values of x that will cause the denominator to equal 0.  To find these values, set the denominator equal to 0 and solve for x.

x - 5 = 0

x = 5

The value of x that is not in the domain of the function is x = 5.