[URGENT]AS level Pure mathematics "Functions" Question?

[Humagai]

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The function g(x) = 4-3sinx is defined for the domain 0.5pie <= x <= A.
iv) State the largest value of A for which g has an inverse .
v) For this value of A, find the value of g^-1 (g inverse) (3)
Best Regards,
Please post fast.

 

[Panchimma]

Its pretty easy .I think the answer is ="3/2 pie"
i am supposing that the previous part of this question was to draw the sine gaph. If u draw the graph , its easy to understand. Basically for a function to have an inverse, it should be one-one , ie there should be only one value of x for each value of y . As sine graph is consecutive waves if u take a point y on the y axis and take corresponding values of x on the graph, there will be a lot of answers. For making it a one to one function, we should restrict the period to only where there will be only one point of intersection of a line from any point y parallel to x axis. This happens at x=3/2 pie in the sine graph. If u cut off the rest of the graph , the function can be seen as being one to one.

Best of luck for your examz...im doing as maths too..