Question

find domain and range f(x)=1/3-2sinx
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Answer 1

For Domain;

3 – 2sinx ≠ 0

2sinx ≠ 3

or sinx≠ 3/2

But, –1 ≤ sinx ≤ 1

So, x ∈ R [Domain]

For Range;

As, –1 ≤ sinx ≤ 1

On multiplying both sides by –2

• –2 ≤ –2sinx ≤ 2

On adding 3 to both the sides

• 1 ≤ 3 – 2sinx ≤ 5

On reciprocating each term

• 1/5 ≤ f(x) ≤ 1

So,

f(x) ∈ [ 0.2, 1 ] (Range)