If f(x)= beginBmatrix[x], text if -3

Question

If f(x)= beginBmatrix[x], text if -3< x ≤-1 |x|, text if -1< x< 1 |[x]|, text if 1 ≤ x< 3 endBmatrix the set of values of x, where f(x) ≥ 0, (where [.] represents the greatest integer function) is (A) (-1,3) (B) [-1,3) (C) (-1,3] (D)  [-1,3]

Tardigrade Admin · Accepted Answer

Given, f x=x if -3< x ≤-1 x if -1< x< 1 x if 1 ≤ x< 3 When -3< x ≤-1, f x=x ⇒ f x<0 When -1< x< 1 , f x=x ⇒ f x ≥ 0 When 1 ≤ x< 3, f x=x ⇒ f x ≥ 1 ∴ The set x: f x ≥ 0=(-1,3).

Q. If $f (x) = ⎩ ⎨ ⎧ [x], if - 3 < x \leq - 1 ∣ x ∣, if - 1 < x < 1 ∣ [x] ∣, if 1 \leq x < 3 ⎭ ⎬ ⎫$
the set of values of $x$ , where $f (x) \geq 0$ , (where [.] represents the greatest integer function) is

$(- 1, 3)$

$[- 1, 3)$

$(- 1, 3]$

$[- 1, 3]$

Given,
$f x = x$ if $- 3 < x \leq - 1 x$ if $- 1 < x < 1 x$ if $1 \leq x < 3$
When $- 3 < x \leq - 1, f x = x \Rightarrow f x < 0$
When $- 1 < x < 1, f x = x \Rightarrow f x \geq 0$
When $1 \leq x < 3, f x = x \Rightarrow f x \geq 1$
$∴$ The set $x : f x \geq 0 = (- 1, 3)$ .

Q. If f(x)=⎩⎨⎧​[x], if −3<x≤−1∣x∣, if −1<x<1∣[x]∣, if 1≤x<3​⎭⎬⎫​ the set of values of x, where f(x)≥0, (where [.] represents the greatest integer function) is

(−1,3)

[−1,3)

(−1,3]

[−1,3]