The domain of the function fx-3-1-x-3- is where - denotes the greatest integer function

The correct option is D ℝ [ 3, 2)f(x)=3 1[x+3] For function to be defined, [x+3]≠0 ⇒ [x]+3≠0 (∵ nbsp;[x+ℤ]=[x]+ℤ) ⇒ [x]≠ 3 ⇒ x∉[ 3, 2) ∴ Domain of f(x)=ℝ [ ...

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Standard XII

Mathematics

Greatest Integer Function

The domain of...

Question

The domain of the function $f (x) = 3 - \frac{1}{[x + 3]}$ is
(where [.] denotes the greatest integer function)

R

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R - {- 3}

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R - [- 3, - 2)

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ϕ

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Solution

The correct option is C $R - [- 3, - 2)$
$f (x) = 3 - \frac{1}{[x + 3]}$
For function to be defined,
$[x + 3] \neq 0 \Rightarrow [x] + 3 \neq 0 (∵ [x + Z] = [x] + Z) \Rightarrow [x] \neq - 3 \Rightarrow x \notin [- 3, - 2)$
$∴$ Domain of $f (x) = R - [- 3, - 2)$

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The domain of the function f(x)=3−1[x+3] is (where [.] denotes the greatest integer function)

The correct option is C R−[−3,−2)f(x)=3−1[x+3] For function to be defined, [x+3]≠0⇒[x]+3≠0 (∵[x+Z]=[x]+Z)⇒[x]≠−3⇒x∉[−3,−2) ∴ Domain of f(x)=R−[−3,−2)

The domain of the function $f (x) = 3 - \frac{1}{[x + 3]}$ is
(where [.] denotes the greatest integer function)

The correct option is C $R - [- 3, - 2)$
$f (x) = 3 - \frac{1}{[x + 3]}$
For function to be defined,
$[x + 3] \neq 0 \Rightarrow [x] + 3 \neq 0 (∵ [x + Z] = [x] + Z) \Rightarrow [x] \neq - 3 \Rightarrow x \notin [- 3, - 2)$
$∴$ Domain of $f (x) = R - [- 3, - 2)$