Final answer:
To complete the statement, we need to compare the function f(x) = 2x² + 5/(x-2) with another function. We can analyze the behavior of both functions as x approaches positive and negative infinity to determine which is greater.
Step-by-step explanation:
To complete the statement, we need to compare the function f(x) = 2x² + 5/(x-2) with another function.
Let's compare f(x) with the function g(x) = 2x².
To compare the two functions, we can analyze their behavior as x approaches positive infinity and negative infinity.
As x approaches positive infinity, f(x) will approach the same value as g(x), which is positive infinity. Therefore, we can say that f(x) is greater than g(x) as x approaches positive infinity.
As x approaches negative infinity, both f(x) and g(x) will approach positive infinity. Therefore, we can say that f(x) is also greater than g(x) as x approaches negative infinity.
Based on our analysis, we can conclude that f(x) is greater than g(x) for all x. So, the correct answer to the statement is C. Greater.