Question

Match each function with its domain. 1. S(x) = √x 2. H(x) = √2+x 3. Z(x) = √x-2 4. Q(x) = √2-x 5. V(x) = √-x 6. N(x) = ^3√2-x x ≤ 2 x ≥ -2 x ≥ 0 x ≥ 2 x ≤ 0 All real numbers

Answer 1

Answer:

1. x ≥ 0

2. x ≥ -2

3. x ≥ 2

4. x ≤ 2

5. x ≤ 0

6. All real numbers

Step-by-step explanation:

Domain of square function:

Suppose we have a square function in the following format:

$f(x) = \sqrt[n]{g(x)}$

If n is even, the domain of f(x) is:

$g(x) \geq 0$

Otherwise, if n is odd, the domain of f(x) is all real numbers.

1. S(x) = √x

If n does not appear is that it is 2.

g(x) = x

So the domain is:

$x \geq 0$

2. H(x) = √2+x

g(x) = 2 + x

So

$2 + x \geq 0$

$x \geq -2$

3. Z(x) = √x-2

g(x) = x - 2

$x - 2 \geq 0$

$x \geq 2$

4. Q(x) = √2-x

g(x) = 2 - x

$2 - x \geq 0$

$-x \geq -2$

Multiplying by -1, everything

$x \leq 2$

5. V(x) = √-x

g(x) = -x

Then

$-x \geq 0$

Multiplying by -1

$x \leq 0$

6. N(x) = ^3√2-x

Cubic root(odd number), so all real numbers.