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Please help me finding the range and domain of this modulus function Question no.4

Please help me finding the range and domain of this modulus function
Question no.4

Question Image
Grade:12

1 Answers

Aditya Gupta
2080 Points
2 years ago
Obviously domain is R
Now let |sinx|= siny where y lies in 0 to pi so that |cosx|= cosy
So function becomes 3siny-4cosy
At y=0 it's Value is -4 and at y=pi/2 it's Value is 3
Also f'(y)= 3cosy+4siny >0
So f(y) is an increasing function.
Hence range is [-4,3]

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