Domain of the function f(x) = √2 - 2x - x2 is

Question

Domain of the function f(x) = √2 - 2x - x2 is (A)  - √3 le x le + √3 (B) -1 - √3 le x le -1 + √3 (C) -2 le x le 2  (D)  - 2+ √3 le x le - 2 - √3

Tardigrade Admin · Accepted Answer

Given f(x) = √2 - 2x - x2 ge 0 Now f(x) is well defined when: √2 - 2x - x2 ge 0 or , 2 - 2x - x2 ge 0 or, x2 + 2x - 2 le 0 (x + 1 - √3)(x +1 + √3) le 0 or -1 - √3 le x le - 1 + √3

Q. Domain of the function $f (x) = 2 - 2 x - x^{2}$ is

$- 3 \leq x \leq + 3$

$- 1 - 3 \leq x \leq - 1 + 3$

$- 2 \leq x \leq 2$

$- 2 + 3 \leq x \leq - 2 - 3$

Given $f (x) = 2 - 2 x - x^{2} \geq 0$
Now f(x) is well defined when :
$2 - 2 x - x^{2} \geq 0$
or , $2 - 2 x - x^{2} \geq 0$
or, $x^{2} + 2 x - 2 \leq 0$
$(x + 1 - 3) (x + 1 + 3) \leq 0$
or $- 1 - 3 \leq x \leq - 1 + 3$

Q. Domain of the function f(x)=2−2x−x2​ is

−3​≤x≤+3​

−1−3​≤x≤−1+3​

−2≤x≤2

−2+3​≤x≤−2−3​