Question

Find domain and range of
f(x) =
2-Sin 3x
olunto.​

Answer 1

Answer:

Step-by-step explanation:

Given function is :

●For DOMAIN :

-----------------------

f(x) =1/2-3sinx

Function f(x) is not defined when

=> 2 - sin3x = 0

so , sin3x = 2 ---------(1)

but we know that range of sinx € [ -1, 1 ]

so maximum value of sin3x = 1

therefore sin3x ≠ 2 ( not possible)

=> 2 - sin3x ≠ 0 ------(2)

so from equation (2) we can se tha function is defined for all values of x

=> Domain € R

We know that

-1 < or = (sin3x) < or = 1

#FOR RANGE :

----------------------

now multiplying by -1 we get,

=> 1 ≥ - sin3x ≥ -1

adding 2 we get,

=> 2+1 ≥ 2 - sin3x ≥ 2-1

=> 3 ≥ 2-sin3x ≥ 1

now taking inverse we get,

so Range € [ ⅓ , 1 ]

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