Find the domain and range of 1/(4-cos3x)

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Solution

We know the range of cos3x is [-1,1]

-1 < cos3x < 1
multiply by -1 on all the sides we get ,
1 > -cos3x > -1 (as multiplying by -1 changes the inequality sign)
add 4 on all the sides we get ,
5 > 4 - cos3x > 3
now take the reciprocal of this whole expression we get
1/5 < 1/(4 - cos3x) < 1/3
thus the range of ur required expression is from [1/5 ,1/3]

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