Question

HELP I'M SOOOOOO ANGRYYYYY PLEASE HELPPPP
determine the values of X for which g(x) is defined​

Answer 1

Answer: Any real number x as long as
`x \\e 0` and
`x \\e -(2)/(3)`

In other words, anything but 0 or -2/3 is valid.

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Step-by-step explanation:

Set the denominator equal to zero and solve for x

2(3x^2 + 2x) = 0

3x^2 + 2x = 0

x(3x + 2) = 0

x = 0 or 3x+2 = 0 .... zero product property

x = 0 or 3x = -2

x = 0 or x = -2/3

If either x = 0 or x = -2/3, then the denominator 2(3x^2 + 2x) will be zero. But recall that we cannot have zero in the denominator. Dividing by zero is not allowed. The expression is undefined when we divide by zero.

Therefore, we must exclude x = 0 and x = -2/3 from the domain. Any other real number is valid as an x input.