Let f : R → R be continuous at c ∈ R. Then |f | is continuous at c. Give anexample to show that the reverse is not true

Sorry, there seems to be a misunderstanding. The text you provided is a mathematical statement, not a language. However, I can explain the statement and provide an example.

The statement is saying that if a function f is continuous at a point c, then the absolute value of the function, denoted by |f|, is also continuous at that point.

Continuity at a point means that the limit of the function as it approaches that point is equal to the value of the function at that point. In simpler terms, there are no jumps, breaks, or holes in the function at that point.

Now, let's provide an example to show that the reverse is not true. That is, even if |f| is continuous at a point, it doesn't necessarily mean that f is also continuous at that point.

Consider the function f(x) = x for x < 0 and f(x) = -x for x ≥ 0. This function is not continuous at x = 0 because the limit as x approaches 0 from the left is not equal to the limit as x approaches 0 from the right. However, the absolute value of the function, |f(x)| = |x| for x < 0 and |f(x)| = |-x| = x for x ≥ 0, is continuous at x = 0. This shows that even though |f| is continuous at a point, f may not be.