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Determine the domain of the functiony=|x+2|−1𝑦=|𝑥+2|−1.Select one:A.x⩾−7𝑥⩾−7B.y⩾−1𝑦⩾−1C.y∈R𝑦∈𝑅D.x∈R

Question

Determine the domain of the function

Given the function:
y=∣x+2∣−1 y = |x + 2| - 1

Select one:
A. x≥−7 x \geq -7
B. y≥−1 y \geq -1
C. y∈R y \in \mathbb{R}
D. x∈R x \in \mathbb{R}

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Solution

The domain of a function is the set of all possible input values (often denoted as 'x') which will produce a valid output.

The function given is y = |x+2| - 1.

The absolute value function |x+2| will accept any real number, because it simply reflects negative numbers to positive, and leaves positive numbers as they are.

Then, subtracting 1 from the absolute value will also not restrict the domain, because you can subtract 1 from any real number.

Therefore, the domain of the function is all real numbers, which is represented as x∈R.

So, the correct answer is D. x∈R.

This problem has been solved

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