Identify the restricted values. $$ \frac{t-14}{t^{2}-2 t-24} $$ If there is more than one restricted value, use the "and" button.

Question

UpStudy AI · Accepted Answer

The restricted values are the values of $$ t $$ that make the denominator zero, as the function is undefined for these values.

Given the function:
$$
\frac{t - 14}{t^2 - 2t - 24}
$$

**Step 1: Set the denominator equal to zero and solve for $$ t $$.**
$$
t^2 - 2t - 24 = 0
$$

**Step 2: Factor the quadratic equation.**
$$
(t - 6)(t + 4) = 0
$$

**Step 3: Solve for $$ t $$.**
$$
t - 6 = 0 \quad \Rightarrow \quad t = 6
$$
$$
t + 4 = 0 \quad \Rightarrow \quad t = -4
$$

**Restricted Values:**
$$
t = 6 \quad \text{and} \quad t = -4
$$

So, the restricted values are $$ t = 6 $$ **and** $$ t = -4 $$.
The restricted values are $$ t = 6 $$ and $$ t = -4 $$.

Identify the restricted values. \( \frac{t-14}{t^{2}-2 t-24} \) If there is more than one restricted value, use the "and" button.