Question

find the domain of the following function f(x)=sqrt x-4. write your answer in interval notation.

Answer 1

Answer:

$[4,\infty)$

Step-by-step explanation:

We have been given a function $f(x)=\sqrt{x-4}$. We are asked to find the domain of our given function.

We know that domain of a function is all values of independent variable for which function is defined.

We also know that square root of negative numbers is not defined.

The domain of our given function will be all non-negative values of x as:

$x-4\geq 0$

$x-4+4\geq 0+4$

$x\geq 4$

Therefore, the domain of our given function is all values of x greater than or equal to 4 that is $[4,\infty)$ in interval notation.

Answer 2

Using the concepts of the square root function, it is found that the domain is: $[4, \infty)$

----------------------

The square root function is given by:

$f(x) = \sqrt{g(x)}$

The domain is:

$g(x) \geq 0$

----------------------

In this question, we have:

$f(x) = \sqrt{x - 4}$

Thus:

$g(x) = x - 4$

Then, the domain is:

$x - 4 \geq 0 \rightarrow x \geq 4$

In interval notation, $[4, \infty)$

From the graph given at the end, it can be seen that x assumes values from 4 to infinity.

A similar problem is given at https://brainly.com/question/23826461