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Standard XII
Mathematics
Using Monotonicity to Find the Range of a Function
The range of ...
Question
The range of the function f(x) = sin [x],
−
π
4
≤
x
≤
π
4
where [x] denotes the greatest integer, is
A
{0}
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B
{0, -1}
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C
{0,
±
sin 1}
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D
{0, -
sin 1}
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Solution
The correct option is
D
{0, -
sin 1}
−
π
4
≤
x
<
0
or
0
≤
x
≤
π
4
⇒
[x] =
-
1
or [x] = 0
⇒
sin [x] = sin (
-
1) or sin 0
⇒
sin [x] = - sin 1 or 0
∴
R (f) = {-sin 1, 0}
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