What is the Domain and Range of the function f(x)

Question

2 years ago

14

le="\sqrt{x-7} +9" alt="\sqrt{x-7} +9" align="absmiddle" class="latex-formula">?

1 answer:

omeli [17] · Answer 1 · 2023-08-12T14:11:28+03:00

For the given function, the domain is D : { x ≥ 7} and the range is R: { y ≥ 9}

<h3>How to get the domain and range?</h3>

Here we have a square root, remember that the argument of the square root must be equal or larger than zero, so the domain is such that:

x - 7 ≥ 0.

Solving for x we get:

x ≥ 0 + 7

Then the domain is:

x ≥ 7

To get the range, we evaluate in the minimum of the domain:

f(7) = √(7 - 7) + 9 = 9

Then the range is the set of all values larger than 9, because the function is increasing.

So the range is R: y ≥ 9.

If you want to learn more about domain and range:

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