Question

assignment 5.6 rational functions
score: 1/10 answered: 1/10
question 2
given the function, find its domain.
$f(x) = \frac{5x + 7}{x^2 + 15x + 50}$
the domain is all real numbers except x =
if there is more than one answer, write it as a list, using commas to separate your answers.
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Explanation:

Step1: Factor the denominator

We have the denominator \(x^{2}+15x + 50\). We need to find two numbers that multiply to \(50\) and add up to \(15\). The numbers are \(10\) and \(5\). So, we can factor the quadratic as follows:

$$x^{2}+15x + 50=(x + 10)(x+5)$$

Step2: Find the values that make the denominator zero

To find the values of \(x\) that make the denominator zero, we set each factor equal to zero:

1. For \(x + 10=0\), we solve for \(x\) and get \(x=- 10\).
2. For \(x + 5=0\), we solve for \(x\) and get \(x=-5\).

Since the function is a rational function, the domain is all real numbers except the values that make the denominator zero. So the domain is all real numbers except \(x=-10\) and \(x = - 5\).

Answer:

-10, -5