Final answer:
The equation of the oblique asymptote for the function g(x)= (x² + x + 4)/(x - 1) is found by dividing the numerator by the denominator; it is y = x + 2.
Step-by-step explanation:
The oblique asymptote for the function g(x)= (x² +x+4)/(x-1) can be found by performing long division or synthetic division of the numerator by the denominator, since the degree of the numerator is one higher than the degree of the denominator. The result of this division will provide the equation of the oblique asymptote.
To find the oblique asymptote, divide x² + x + 4 by x - 1. The quotient will be of the form ax + b, which represents the equation of the asymptote since the remainder will become insignificant as x approaches infinity.
Step-by-step Division Process:
1. Divide x² by x to get x.
2. Multiply x - 1 by x to get x² - x.
3. Subtract x² - x from x² + x to get 2x.
4. Bring down the + 4 and divide 2x + 4 by x to get 2.
5. The equation of the oblique asymptote is thus y = x + 2.
Therefore, the equation of the oblique asymptote for the function g(x) is y = x + 2.