The domain of the function y=(1/√|x|-x) is:

Question

The domain of the function y=(1/√|x|-x) is: (A)  (-∞ , 0)  (B)  (+∞ , 0)  (C)  (-∞ , -1)  (D)  (-∞ , ∞ )

Tardigrade Admin · Accepted Answer

Given, y=(1/√|x|-x) When x ≥ 0 y=(1/√x-x)=∞ (not defined) When x < 0 y=(1/√-x-x)=(1/√-2 x) ∴ Given function is defined for every negative values of x . ∴ Required domain is (-∞, 0).

Q. The domain of the function $y = \frac{1}{∣ x ∣ - x}$ is:

$(- \infty, 0)$

$(+ \infty, 0)$

$(- \infty, - 1)$

$(- \infty, \infty)$

Given, $y = \frac{1}{∣ x ∣ - x}$
When $x \geq 0 y = \frac{1}{x - x} = \infty$ (not defined)
When $x < 0 y = \frac{1}{- x - x} = \frac{1}{- 2 x}$
$∴$ Given function is defined for every negative values of $x$ .
$∴$ Required domain is $(- \infty, 0)$ .

Q. The domain of the function y=∣x∣−x​1​ is:

(−∞,0)

(+∞,0)

(−∞,−1)

(−∞,∞)