function and trig

Question

The function g: x ----> a + bsinx where

a=4 and b=2

is defined for the domain pi/2 ≤ x ≤ k.

 

Find the largest value of k for which g(x) has an inverse.

Answer 1

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Answer 2

The graph of g begins at x=pi/2 and g(x) there = a+b.  For x values proceedin to the right, the graph will descend, passing through (pi,a) and continuing to descend until (3pi/2,a-b).

 

The graph would then go back up from here, if x were to exceed 3pi/2--and then the graph would not satisfy the Horizontal Line Test (necessary for inverse).  Therefore k = 3pi/2.