Question

18. Domain of f(x) =
3-lx
is
V1x1-7​

Answer 1

EXPLANATION.

$\implies \sqrt{\dfrac{3 - |x|}{|x| - 7} }$

As we know that,

From denominator never be = 0.

⇒ |x| - 7 ≠ 0.

⇒ |x| ≠ 7.

⇒ x ≠ +7, -7.

Case = 1.

⇒ For x ≥ 0.

⇒ 3 - x/x - 7 ≥ 0.

⇒ x - 3/x - 7 ≤ 0.

Find zeroes of the equation, we get.

⇒ x - 3 = 0.

⇒ x = 3. - - - - - (1).

⇒ x - 7 = 0.

⇒ x = 7. - - - - - (2).

Put the value in the wavy curve method, we get.

⇒ x ∈ [3,7). - - - - - (a).

Case = 2.

⇒ For x ≤ 0.

⇒ 3 - (-x)/(-x) - 7 ≤ 0.

⇒ 3 + x/-x - 7 ≤ 0.

⇒ x + 3/x + 7 ≤ 0.

Find Zeroes of the equation, we get.

⇒ x + 3 = 0.

⇒ x = - 3. - - - - - (1).

⇒ x + 7 = 0.

⇒ x = - 7. - - - - - (2).

Put this point on the wavy curve method, we get.

⇒ x ∈ [-3,-7). - - - - - (b).

Take union of equation (a) ∪ (b), we get.

⇒ x ∈ [-3,-7) ∪ [3,7).