Q. 3 D3.8( 70 Votes )
Examine the following functions for continuity.
f (x) = | x – 5|
Answer :
The given function is 
The function f is defined at all points of the real line.
Let k be the point on a real line.
Then, we have 3 cases i.ee, k < 5, or k = 5 or k >5
Now, Case I: k<5
Then, f(k) = 5 – k
= 5 – k = f(k)
Thus, 
Hence, f is continuous at all real number less than 5.
Case II: k = 5
Then, f(k) = f(5) = 5 – 5 = 0
= 5 – 5 = 0
= 5 – 5 = 0
Hence, f is continuous at x = 5.
Case III: k > 5
Then, f(k) = k – 5
= k – 5 = f(k)
Thus, 
Hence, f is continuous at all real number greater than 5.
Therefore, f is a continuous function.
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