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please help!! Find the domain and range of the following function ƒ(x) = 5|x - 2| + 4
Domain: (-∞,∞) Range: (4,∞)
Domain: [4,8) Range: (-∞,∞)
Domain: (4,∞) Range: (-∞,∞)
Domain: (-∞,∞) Range: [4,∞)

Respuesta :

jbmow

Answer:

There are no restrictions on x, so the domain is (-∞,∞)

When x = 2, 5|x - 2| = 0, so the range is [4,∞)

Step-by-step explanation:

varshamittal029

The domain and range of the function ƒ(x) = 5|x - 2| + 4 is (-∝, ∝) and [4, ∝) respectively. So, the 4th option is correct.

Domain and range of a function:

A function's domain is the set of all values for which the function is defined, and its range is the set of all values that the function takes.

How to solve this problem?

The given function is ƒ(x) = 5|x - 2| + 4.

This function is not undefined for any x-values. So, the domain of this function is (-∝,∝).

We know that

|x - 2| ≥ 0

i.e. 5|x - 2| ≥ 0

i.e. 5|x - 2| + 4 ≥ 4

i.e. f(x) ≥ 4

So, the range of this function is [4,∝).

Therefore, the domain and range of the function ƒ(x) = 5|x - 2| + 4 is (-∝, ∝) and [4, ∝) respectively. So, the 4th option is correct.

Learn more about domain and range of a function here -

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