Question

What are the domain and range of this function? Domain: all real numbers; Range: y ≥ −4 Domain: −2 ≤ x ≤ 2; Range: y ≥ −4 Domain: x ≥ −4; Range: all real numbers Domain: x ≥ 0; Range y ≥ 0

Answer 1

Answer:

Domain ; all real numbers

Step-by-step explanation:

For the function Y = cuberoot(x-2) + 4

The domain is the set of all possible values of the independent variable for which the function is real and defined

The range is the set of possible values of the dependent variable for which a function is defined. after the substitution of the domain.

from the function of Y, it has no undefined points as such no domain or constrained domain, therefore domain in this case = -infinity < x < infinity

for the range, solution = -infinity < f(x) < infinity, this implies that both the domain and range are REAL NUMBERS

Answer 2

The domain and the range of a function are the set of input and output values the function can take

The domain of the given function $\mathbf{y = \sqrt[3]{x-2} + 4}$ is all real numbers, and the range is all real numbers.

The function is given as:

$\mathbf{y = \sqrt[3]{x-2} + 4}$

The parent function of the above function is:

$\mathbf{y = \sqrt[3]{x} }$ -- a cubic function

The range and the domain of a cubic function are the set of all real numbers, as there are no restrictions on the input and the output values

Hence, the domain of the given function $\mathbf{y = \sqrt[3]{x-2} + 4}$ is all real numbers, and the range is all real numbers.

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