The above graph shows the curves of and . Clearly, the line is tangent to both the curves. But there exists another such straight line which is tangent to both the curves. Find the equation of the line.
If the line can be represented in the form , such that and are positive integers and , enter your answer as .
Notation: denotes the absolute value function.
If , then in which interval is the function decreasing?
Details:
represents sawtooth function. That is,
Let , where , and are real numbers. In order for to be invertible, and must be related as: , where , and are also real numbers.
Find the mimimum value of .
How many real solutions exist for the equation above?