Question: Is the function f(x) = 1/(x-1) continuous at x = 1?
Options:
Yes
No
Only left continuous
Only right continuous
Correct Answer: No
Solution:
The function f(x) = 1/(x-1) is not defined at x = 1, hence it is discontinuous at that point.
Is the function f(x) = 1/(x-1) continuous at x = 1?
Practice Questions
Q1
Is the function f(x) = 1/(x-1) continuous at x = 1?
Yes
No
Only left continuous
Only right continuous
Questions & Step-by-Step Solutions
Is the function f(x) = 1/(x-1) continuous at x = 1?
Step 1: Identify the function we are examining, which is f(x) = 1/(x-1).
Step 2: Determine the value of x we are interested in, which is x = 1.
Step 3: Substitute x = 1 into the function: f(1) = 1/(1-1).
Step 4: Calculate the denominator: 1 - 1 = 0.
Step 5: Since we cannot divide by zero, f(1) is undefined.
Step 6: A function must be defined at a point to be continuous there.
Step 7: Since f(1) is undefined, the function is not continuous at x = 1.
Continuity of Functions – Understanding whether a function is continuous at a given point involves checking if the function is defined at that point and if the limit exists and equals the function's value.
Undefined Points – Recognizing that a function is discontinuous at points where it is not defined.
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