The function f(x) = 1/(x-1) is continuous on which of the following intervals?

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Question: The function f(x) = 1/(x-1) is continuous on which of the following intervals?

Options:

Correct Answer: (1, ∞)

Solution:

The function f(x) = 1/(x-1) is discontinuous at x = 1, hence it is continuous on (1, ∞).

The function f(x) = 1/(x-1) is continuous on which of the following intervals?

The function f(x) = 1/(x-1) is continuous on which of the following intervals?

Step 1: Identify the function given, which is f(x) = 1/(x-1).
Step 2: Determine where the function might be discontinuous. This happens when the denominator is zero.
Step 3: Set the denominator equal to zero: x - 1 = 0.
Step 4: Solve for x: x = 1. This is where the function is discontinuous.
Step 5: Since the function is discontinuous at x = 1, it cannot be continuous at that point.
Step 6: Identify the intervals where the function is continuous. The function is continuous everywhere except at x = 1.
Step 7: The intervals where the function is continuous are (-∞, 1) and (1, ∞).

Continuity of Functions – Understanding where a function is continuous or discontinuous based on its definition and behavior at specific points.
Identifying Discontinuities – Recognizing points where a function is undefined or has vertical asymptotes, which affect continuity.