Question

Find domain and range - step by step briefly
1) f(x) = √2/√3+x
2) f(x) =√x/√x-1
3) f(x) =√x^2-1/√3
4) f(x) = 4/√2-x^2
5) f (x) = 5
6) f(x) = 1/x^2​

Answer 1

Step-by-step explanation:

1) the domain and range of the following function.

f(x) = 2/ (x + 1)

Solution

Set the denominator equal to zero and solve for x.

x + 1 = 0

= -1

Since the function is undefined when x = -1, the domain is all real numbers except -1. Similarly, the range is all real numbers except 0.

2)The domain of f(x) = √ (6 + x – x2)

Solution

To avoid the square roots of negative numbers, we set the expression inside the radical sign to ≥ 0.

6 + x – x2 ≥ 0 ⟹ x 2 – x – 6≤ 0

⟹ x 2 – x – 6= (x – 3) (x +2) = 0

Therefore, the function is zero if x = 3 or x = -2

Hence the domain: [−2, 3]

3) the domain of f(x) =x/√ (x2 – 9)

Solution

Set the expression within the radical sign to x2 – 9 > 0

Solve for the variable to get;

x = 3 or – 3

Therefore, Domain: (−∞, −3) & (3, ∞)