Question

f(x)=1/5-3sin2x find domain and range

Answer 1

Answer:

Domain: all reals x. Range: −3≤y ≤3. Explanation: y=−3sin(x2) The amplitude is 3. The period (T) = 2πn=2π12=4π. Now you can ...

Answer 2

Step-by-step explanation:

#Hey there!!

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◆Given function is :

$$\begin{lgathered}f(x) = \frac{1}{2 - sin3 x} \\\end{lgathered}$$

●For DOMAIN :

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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

#FOR RANGE :

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$$\begin{lgathered}we \: know \: that \: \\ - 1 \leqslant \sin(3x) \leqslant 1 \\\end{lgathered}$$

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,

$$\frac{1}{3} \leqslant \frac{1}{2 - \sin(3x) } \leqslant 1$$

so Range € [ ⅓ , 1 ]

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