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If f(x) = x2 – 25 and g(x) = x – 5, what is the domain of mc006-1.jpg? all real values of x all real values of x except x = 5 all real values of x except x = –5 all real values of x except x = 5 and x = –5

Verified Answer :

Edufirst

The questions asks for the domain of [f/g](x).

That is f(x) /  g(x) = [x^2 - 25] / [X-5].

The domain of that functions are all the real except those where the denominator becomes zero.

You find those points by doing X - 5 = 0 => x = 5.

Then, the domain of [f/g](x) is all real numbers except x = 5.

The domain of the function f(x)/g(x) is given by:

  • all real values of x.

What is the domain of a function?

The domain of a function is the set that contains all possible input values.

In this problem, the function is:

\(h(x) = \frac{f(x)}{g(x)} = \frac{x^2 - 25}{x - 5}\)

Using subtraction of perfect squares, we have that:

\(f(x) = x^2 - 25 = (x - 5)(x + 5)\)

Then:

\(h(x) = \frac{(x - 5)(x + 5)}{x - 5} = x + 5\)

No restrictions, hence the domain is all real values.

You can learn more about the domain of a function at https://brainly.com/question/10891721

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