If f x -3- x -1-2- x -2- x -5- then the value of f 2-999 iwhere - denotes the greatest integer function

F(x)=3[x+1]+2[x+2]+[x 5] ⇒ f(x)=3([x]+1)+2([x]+2)+[x] 5 (∵ [x+I]=[x]+I, ∀ I∈ℤ) ⇒ f(x)=3[x]+3+2[x]+4+[x] 5 ⇒ f(x)=6[x]+2 ∴ f(2.999)=6[2.999]+2 =6×2+2 =14 ...

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Byju's Answer

Standard XII

Mathematics

Greatest Integer Function

If f x =3[ x ...

Question

If $f (x) = 3 [x + 1] + 2 [x + 2] + [x - 5],$ then the value of $f (2.999)$ is
(where [.] denotes the greatest integer function)

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Solution

$f (x) = 3 [x + 1] + 2 [x + 2] + [x - 5]$
$\Rightarrow f (x) = 3 ([x] + 1) + 2 ([x] + 2) + [x] - 5$
$(∵ [x + I] = [x] + I, \forall I \in Z)$
$\Rightarrow f (x) = 3 [x] + 3 + 2 [x] + 4 + [x] - 5$
$\Rightarrow f (x) = 6 [x] + 2$
$∴ f (2.999) = 6 [2.999] + 2$
$= 6 \times 2 + 2$
$= 14$

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If f(x)=3[x+1]+2[x+2]+[x−5], then the value of f(2.999) is (where [.] denotes the greatest integer function)

f(x)=3[x+1]+2[x+2]+[x−5] ⇒f(x)=3([x]+1)+2([x]+2)+[x]−5 (∵[x+I]=[x]+I, ∀ I∈Z) ⇒f(x)=3[x]+3+2[x]+4+[x]−5 ⇒f(x)=6[x]+2 ∴f(2.999)=6[2.999]+2 =6×2+2 =14

If $f (x) = 3 [x + 1] + 2 [x + 2] + [x - 5],$ then the value of $f (2.999)$ is
(where [.] denotes the greatest integer function)

$f (x) = 3 [x + 1] + 2 [x + 2] + [x - 5]$
$\Rightarrow f (x) = 3 ([x] + 1) + 2 ([x] + 2) + [x] - 5$
$(∵ [x + I] = [x] + I, \forall I \in Z)$
$\Rightarrow f (x) = 3 [x] + 3 + 2 [x] + 4 + [x] - 5$
$\Rightarrow f (x) = 6 [x] + 2$
$∴ f (2.999) = 6 [2.999] + 2$
$= 6 \times 2 + 2$
$= 14$