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Let h be a strictly increasing continuous function. Show that its inverse, denoted by $h^{-1}$, is also a strictly increasing function. How to approach this question? $\endgroup$ 2
An inverse head and shoulders, also called a "head and shoulders bottom", is similar to the standard head and shoulders pattern, but inverted: with the head and shoulders top used to predict reversals in downtrends. This pattern is identified when the price action of a security meets the following characteristics: the price falls to a trough and then rises; the price falls below the former trough and then rises again; finally, the price falls again but not as far as the second trough. Once the final trough is made, the price heads upward, toward the resistance found near the top of the previous troughs. Image by Sabrina Jiang © Investopedia 2020
Investors typically enter into a long position when the price rises above the resistance of the neckline. The first and third trough are considered shoulders and the second peak forms the head. A move above the resistance, also known as the neckline, is used as a signal of a sharp move higher. Many traders watch for a large spike in volume to confirm the validity of the breakout. This pattern is the opposite of the popular head and shoulders pattern but is used to predict shifts in a downtrend rather than an uptrend. A suitable profit target can be ascertained by measuring the distance between the bottom of the head and the neckline of the pattern and using that same distance to project how far the price may move in the direction of the breakout. For example, if the distance between the head and neckline is ten points, the profit target is set ten points above the pattern's neckline. An aggressive stop-loss order can be placed below the breakout price bar or candle. Alternatively, a conservative stop-loss order can be placed below the right shoulder of the inverse head and shoulders pattern. An inverse head and shoulders pattern is comprised of three component parts:
A buy stop order can be placed just above the neckline of the inverse head and shoulders pattern. This ensures the investor enters on the first break of the neckline, catching upward momentum. Disadvantages of this strategy include the possibility of a false breakout and higher slippage in relation to order execution. An investor can wait for the price to close above the neckline; this is effectively waiting for confirmation that the breakout is valid. Using this strategy, an investor can enter on the first close above the neckline. Alternatively, a limit order can be placed at or just below the broken neckline, attempting to get an execution on a retrace in price. Waiting for a retrace is likely to result in less slippage; however, there is the possibility of missing the trade if a pullback does not occur. The opposite of an inverse head and shoulders chart is the standard head and shoulders, used to predict reversals in up-trends. This pattern is identified when the price action of a security meets the following characteristics: the price rises to a peak and then falls; the price rises above the former peak and then falls again; finally, the price rises again but not as far as the second peak. Once the final peak is made, the price heads downward, toward the resistance found near the bottom of the previous peaks. Like all charting patterns, the ups and downs of the head and shoulders pattern tell a very specific story about the battle being waged between bulls and bears. The initial decline and subsequent peak represent the building momentum of the prior bearish trend into the first shoulder portion. Wanting to sustain the downward movement as long as possible, bears try to push the price back down past the initial trough after the shoulder to reach a new low (the head). At this point, it is still possible that bears could reinstate their market dominance and continue the downward trend. However, once the price rises a second time and reaches a point above the initial peak, it is clear that bulls are gaining ground. Bears try one more time to push the price downward but succeed only in hitting the lesser lower reached in the initial trough. This failure to surpass the lowest low signals the bears' defeat and bulls take over, driving the price upward and completing the reversal.
The inverse head and shoulders chart is thought to predict a bearish-to-bullish trend reversal and signals that a downward trend is nearing its end. Investors consider it to be among the most reliable trend reversal patterns.
The most common entry point is a breakout of the neckline, with a stop below (market bottom) or above (market top) the right shoulder. The profit target is the difference between the high and low with the pattern added (market bottom) or subtracted (market top) from the breakout price. The system is not perfect, but it does provide a method of trading the markets based on logical price movements.
The neckline is the level of support used to determine where to place orders. To identify the neckline, first locate the left shoulder, head, and right shoulder on the chart. In the inverse head and shoulders pattern (market bottom), we connect the high after the left shoulder with the high created after the head.
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