Find the domain and range of the following functions : 1)f(x)+root x^2-4 2)f(x)+root 16-x^2

1)  (-∞, -2) ∪ (2, ∞);  2) (-4, 4)

Step-by-step explanation:

1)

f(x)+root x^2-4 => f(x) = √(x^2 - 4)

Since the domain of the square root function is [0, ∞), we must determine the intervals on which x^2 - 4 is ≥ 0.  First determine the x values at which x^2 - 4 = 0:  (x-2)(x+2) = 0 produces two results:  x = -2 and x = 2.

These two numbers determine three intervals on the real number line:

(-∞, -2), (-2, 2), (2, ∞).  Choosing a "test number" from each interval, we get -3, 0 and 3.  All that remains to do now is to determine whether x^2 - 4 is positive or negative on each interval.

Case 1:  test number -3:  Is (-3)^2 - 4 positive or neg?  It's positive.

Case 2:  test number 0.  Is (0)^2 -4 positive or neg?  It's negative.  Reject this interval.

Case 3:  test number +3:  Is (+3)^2 - 4 positive or neg?  It's positive.

Thus,  f(x) = √(x^2 - 4) is defined on (-∞, -2) ∪ (2, ∞); this is the domain.

2) f(x) = √(16 - x^2).  Domain?  We go thru steps similar to those above.  16 - x^2 factors into (4 - x)(4 + x); the roots are 4 and -4, and the number intervals are (-∞, -4), (-4, 4), (4, ∞)

Case 1:  Is the radicand (x^2 - 4) + or - on (-∞, -4)?

Choose the test number -6 from the interval  (-∞, -4).   (16 - x^2) is negative on this interval, so (-∞, -4) is NOT part of the domain of  f(x) = √(16 - x^2).  Next, choose the test number 0; you'll find that  f(x) = √(16 - x^2). is positive, so (-4, 4) IS part of the domain of f(x) = √(16 - x^2).  Choosing the test number +6, you'll find that (16 - x^2) is negative, so (4, ∞) is NOT part of the domain of f(x) = √(16 - x^2).

Conclusion:  the domain of f(x) = √(16 - x^2) is (-4, 4).

answer

false

explanation

these practices describe the manner the land use outcome is attained. land management methods implemented by corporations are a mandatory because they are a driver for better land use results economically, socially and environmentally. corporations are required to understand the connection between land use , and land management practices to support sustainable land use policies

ok so the answer to your question is simple as long as you look at the different dimensions that contain the exemplary letters that combined in the right order give you words that eventually within the 5th dimension will conform and give you the correct answer to your question. hope i , stop looking at this easily, look at it with a spectral view.

step-by-step explanation:

told you