Let be any function. Define by for all Then is:
continuous if is continuous
Determine the relationship between .
We have,
This means that will always have a positive value. It will always lie in the quadrant.
A function is said to be continuous if the graph can be drawn without lifting the pen, off the paper i.e it should have no breaks.
Now, if is continuous, then its modulus will also be continuous.
Therefore will also be continuous, so Option (C) holds true.
Hence, the correct answer is Option (C).