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Question

Let f be a function defined as f(x)=3+2sinx94sin2x. Then which of the following option(s) is (are) CORRECT?

A
Domain of f is R
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B
Domain of f is R{32}
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C
Range of f is [15,1]
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D
Range of f is [13,1]
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Solution

The correct options are
A Domain of f is R
C Range of f is [15,1]
f(x)=3+2sinx94sin2x
=3+2sinx(3+2sinx)(32sinx)
=132sinx (3+2sinx0, xR)
f(x)=132sinx
Denominator >0 for all real values of x
Since, f(x) is defined for all xR
Domain is R

We know that
1sinx1
22sinx2
132sinx5
15132sinx1
Range is [15,1]

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