Final answer:
The function f(x) = (2x²+3x-2)/(x+1) has a hole at x = -1.
Step-by-step explanation:
The function f(x) = (2x²+3x-2)/(x+1) represents a rational function. To find the holes, we need to determine the values of x that make the denominator equal to zero. In this case, the denominator is x+1, so the hole occurs at x = -1. To confirm this, we can simplify the function by factoring the numerator and canceling common factors with the denominator. By doing this, we find that the function simplifies to f(x) = 2x-1. This confirms that there is a hole at x = -1.