Question

Determine the domain of the function.

Answer 1

Answer:

The domain of the function is:

                   x ≥ -4, x ≠ -2, x ≠ 5

Step-by-step explanation:

Domain of a function--

A domain of a function is the set of all the input values i.e. the x-values for which a function is defined.

Here we are given a function f(x) as follows:

 $f(x)=\dfrac{\sqrt{x+4}}{(x+2)(x-5)}$

Now, we know that the domain of the function depends on the denominator as well as domain of the square root function.

  Since, a rational function is defined at the points excluding the zero of the denominator function.

i.e.

$x\neq -2,5$

Also, a square root function is defined for all the non-negative values of the function inside the radical sign.

i.e.

$x+4\geq 0\\\\i.e.\\\\x\geq -4$

                     Hence, the domain is:

                  x ≥ -4, x ≠ -2, x ≠ 5

Answer 2

Answer:

  The marked answer is correct.

Step-by-step explanation:

The domain of the function is limited to those values of x for which the function is defined. The value under the radical must be non-negative (x ≥ -4), and the denominator must not be zero (x ≠ -2 or 5).

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For the purpose here, the square root of a negative number is undefined, as is division by zero.