Question. Number of points of discontinuity of the function \(f(x)=\frac{1}{x−5},x\neq 5\) is :

ExplanationStep 1: Check for Points of Discontinuity

A function is discontinuous at points where:

1. It is not defined.
2. The left-hand limit (LHL) and right-hand limit (RHL) do not match or are not finite.

The given function is undefined at \(x=5\) as the denominator becomes zero, leading to an infinite discontinuity.

Step 2: Verify if There Are Other Discontinuities

The function is well-defined and continuous everywhere else because it is a simple rational function(except \(x=5\))

Step 3: Conclusion

Since there is only one point where the function is not defined (\(x=5\)x=5), the number of points of discontinuity is 1.