Find the domain of the following rational function.
R(x) = -3x^2 / x^2 + 2x - 48
(x+8)(x-6)
So the domain is x cannot be 8 or -6. Am I correct?
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you factored the bottom correctly to
(x+8)(x-6)
now each of those can't be zero
x+8 ≠ 0
x ≠ -8
likewise x ≠ 6
notice the sign inside the bracket changed as you set them equal to x
Yes, you are correct. The domain of the rational function R(x) is all real numbers except those that make the denominator equal to zero. In this case, the denominator is (x + 8)(x - 6), so we need to find the values of x that make this expression equal to zero.
Setting each factor equal to zero, we find that x + 8 = 0 gives x = -8, and x - 6 = 0 gives x = 6.
Therefore, the domain of R(x) is all real numbers except x = -8 and x = 6.
Yes, you are correct. The domain of a rational function is the set of all real numbers that the variable (in this case, x) can take on without causing any division by zero or other mathematical inconsistencies. To find the domain, we need to determine the values of x that would make the denominator equal to zero.
In this case, the denominator of the rational function is (x+8)(x-6). To find the values that make the denominator zero, we set each factor equal to zero and solve for x:
x + 8 = 0 ---> x = -8
x - 6 = 0 ---> x = 6
Therefore, the values -8 and 6 make the denominator zero, which would result in division by zero. Therefore, x cannot be -8 or 6. Hence, the domain of the rational function R(x) is all real numbers except x = -8 and x = 6.