Question

Find the domain of the following ​: -

Answer 1

Step-by-step explanation:

(11)

Given: f(x) = (x - 1)/|x - 1|

Set the denominator and solve.

⇒ |x - 1| = 0

⇒ x - 1 = 0

⇒ x = 1

The domain is : (-∞,1) ∪ (1,∞)

(14)

Given: f(x) = √x - 3 + √7 - x

Set inside ≥ 0 and solve it.

(i)

x - 3 ≥ 0

x ≥ 3

(ii)

√7 - x ≥ 0

x ≤ 7

Interval Notation: [3,7]

(17)

Given: f(x) = 1/√2x - 3

√f(x) = f(x) ≥ 0.

⇒ 2x - 3 ≥ 0

⇒ 2x ≥ 3

⇒ x ≥ 3/2

Well, it is also a rational function. Vertical symptotates can be found by setting the value of denominator to 0 and solving for x.

⇒ √2x - 3 = 0

⇒ 2x - 3 = 0

⇒ 2x = 3

⇒ x = (3/2)

The Domain is: (3/2, ∞).

Hope it helps!

Answer 2

hope it helps................