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F(x) =x^2+6x+5/x^2-9 find all values of x that are not in the domain of f

Sagot :

Answer:

To determine the values of \( x \) that are not in the domain of \( f(x) = \frac{x^2 + 6x + 5}{x^2 - 9} \), we identify where the denominator is zero because division by zero is undefined.

The denominator of \( f(x) \) is \( x^2 - 9 \). We set the denominator equal to zero to find the values where \( f(x) \) is undefined:

\[ x^2 - 9 = 0 \]

Solving for \( x \):

\[ x^2 = 9 \]

\[ x = \pm 3 \]

Therefore, \( x = 3 \) and \( x = -3 \) are the values where \( f(x) \) is not defined because they make the denominator zero.

Step-by-step explanation:

- The function \( f(x) \) is undefined where the denominator \( x^2 - 9 \) equals zero because division by zero is not allowed in mathematics.

- By solving \( x^2 - 9 = 0 \), we find that \( x = \pm 3 \).

- Hence, \( x = 3 \) and \( x = -3 \) are the values where \( f(x) \) is undefined, indicating these points are outside the domain of the function \( f(x) \).