Number 8 a&b please!

  a. domain: (-∞, -2] ∪ [2, ∞); range: [0, ∞)

  b. domain: (-∞, ∞); range: [2, ∞)

Step-by-step explanation:

In each case, the domain is the set of x-values for which the function is defined. A square root function will be defined where its argument is non-negative.

The range of the function is the set of values it can produce as output. A square root function cannot produce negative values. The minimum value it can produce will depend on the argument.

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a. The function is defined where ...

  x² -4 ≥ 0

  x² ≥ 4

  |x| ≥ 2 . . . . take the square root

  x ≤ -2 ∪ 2 ≤ x . . . . . the domain of the function

The value of x² -4 can be any non-negative number, so ...

  0 ≤ y < ∞ . . . . . the range of the function

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b. The function is defined where ...

  x² +4 ≥ 0

True for all values of x.

  -∞ < x < ∞ . . . . . the domain of the function

The value of x² +4 cannot be less than 4, so the function value cannot be less than √4 = 2.

  2 ≤ x < ∞ . . . . . the range of the function