The function $$ f $$ is defined as follows. $$ f(x)=\frac{x^{2}-9 x+8}{x^{2}-12 x+36} $$ Find $$ f(6) $$. Simplify. your answer as much as possible. If applicable, click on "Undefined".

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UpStudy AI · Accepted Answer

The function is given as
$$
f(x)=\frac{x^{2}-9x+8}{x^{2}-12x+36}.
$$

**Step 1. Factor the numerator and the denominator if possible.**

The numerator can be factored as
$$
x^{2}-9x+8 = (x-1)(x-8).
$$

The denominator is a perfect square:
$$
x^{2}-12x+36 = (x-6)^2.
$$

**Step 2. Write the function in its factored form.**

Thus, the function becomes
$$
f(x)=\frac{(x-1)(x-8)}{(x-6)^2}.
$$

**Step 3. Substitute $$ x=6 $$ into the function.**

When $$ x=6 $$:
$$
\text{Numerator} = (6-1)(6-8) = 5 \times (-2) = -10,
$$
$$
\text{Denominator} = (6-6)^2 = 0^2 = 0.
$$

**Step 4. Analyze the result.**

Because the denominator is $$ 0 $$ when $$ x=6 $$ and the numerator is non-zero, the expression is undefined at $$ x=6 $$.

Thus, the value of $$ f(6) $$ is
$$
\text{Undefined}.
$$
$$ f(6) $$ is undefined.

The function \( f \) is defined as follows. \[ f(x)=\frac{x^{2}-9 x+8}{x^{2}-12 x+36} \] Find \( f(6) \). Simplify. your answer as much as possible. If applicable, click on "Undefined".

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