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The function f(x)-->4-3sinx is defined for the domain 0≤x≤2pi


Find the set of values of k for which the equation f(x)=k has no solution

Verified Answer :

1--- f(x) = 4 - 3 sin x = 2 
-3 sin x = -2 
sin x = 2/3 
x ≈ 0.7297276562... ≈ 0.73 

2--- -1 ≤ sin x ≤ 1 
-3 ≤ 3 sin x ≤ 3 
3 ≥ -3 sin x ≥ -3 
7 ≥ 4 - 3 sin x ≥ 1 

If k < 1 or k > 7, there is no solution. 

3--- A = 3π/2 

4--- g(x) = 4 - 3 sin x = y 
4 - 3 sin y = x 
4 - x = 3 sin y 
(4 - x)/3 = sin y 
sin^-1 (4 - x)/3 = y= g^-1 

g^-1 (3) = sin^-1 (4 - 3)/4 = sin^-1 1/4 = 2.8017557... ≈ 2.802

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