Question

""ques----find the domain and range of the function f (x)= 1/2-sin3x
.....a proper solution needed!!....

chapter -:relation n functions

class-11th....""

Answer 1

$\bf \huge{hey!!!}$

Solution is refered to the attachment ✔

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$\green{hope \: it \: helps \: you \: }$

$\underline{Rajukumar111}$

Answer 2

$= > f(x) = \frac{1}{2 - sin3x}$
Here,

=> 2 - sin3x ≠ 0

then

=> 2 ≠ sin3x

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As

=> -1 ≤ sin3x ≤ 1
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» So f(x) is defined for all values of x
» Domain = R, all real number.
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We have :-

$= > - 1 \leqslant sin3x \leqslant 1 \\ \\ = > - 1 \leqslant - sin3x \leqslant 1 \\ \\ = > 2 - 1 \leqslant 2 - sin3x \leqslant 2 + 1 \\ \\ = > 1 \leqslant 2 - sin3x \leqslant 3 \\ \\ = > \frac{1}{1} \geqslant 2 - sin3x \geqslant \frac{1}{3} \\ \\ = > \frac{1}{3} \leqslant 2 - sin3x \leqslant \frac{1}{1}$

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» $RANGE = [ \frac{1}{3} ,1]$
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