To sketch: The graph of and determine the value of a from the graph for which exists.
The function .
Draw the graph of as follows.
Draw the graph of 1 + sin x curve to the left of vertical axis since the interval is restricted that x < 0. Then draw the cosine curve between the interval and then draw the sine curve for the interval .
The graph of is shown below in Figure 1.
From Figure 1, it is observed that the graph of lies to the left of the vertical axis, the graph of lies to the left of and the graph of the lies to the right of .
Also notice that, and .
Hence, does not exist.
Therefore, it can be concluded that exists every values of a excluding .
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