Given: $$ f(x)=\frac{3 x-2}{x^{2}+10 x+25} $$ Determine the values of $$ x $$ for which $$ f(x) $$ is defined

Question

UpStudy AI · Accepted Answer

To determine the values of x for which the function is defined, we need to ensure that the denominator is not equal to zero.

The denominator is:  
  x² + 10x + 25

We can factor this quadratic expression:

x² + 10x + 25 = (x + 5)²

The denominator is zero when (x + 5)² = 0, which gives:  
  x + 5 = 0  
  x = -5

Thus, the function f(x) is undefined at x = -5. For all other values of x, the function is defined.

Answer: f(x) is defined for all real numbers except x = -5.
f(x) is defined for all real numbers except x = -5.

Given: \( f(x)=\frac{3 x-2}{x^{2}+10 x+25} \) Determine the values of \( x \) for which \( f(x) \) is defined