Write a piecewise function that is equivalent to (x)= -2/x-2/
To write a piecewise function equivalent to f(x) = -2/(x-2), we need to consider the two possible intervals of x values where the function may have different expressions.
Let's break it down into two cases:
Case 1: When x ≠ 2 (x is not equal to 2)
In this case, the function f(x) = -2/(x-2) has a defined value. We can simply write the function as:
f(x) = -2/(x-2)
Case 2: When x = 2, which is the critical point in the denominator
At x = 2, the denominator (x-2) becomes 0, making the original function undefined. However, we can specify a different expression for the function when x is equal to 2. Let's say we want the value of f(x) to be a certain constant value, C, when x = 2. Then the function can be written as:
f(x) = C (for x = 2)
So now we have a piecewise function:
f(x) = {
-2/(x-2) (for x ≠ 2)
C (for x = 2)
}
To find the specific value of C when x = 2, we need more information. Without any further details, we cannot determine the exact value of C.