Q. 61 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 47– 62, find the domain of each function. 

$P\left(t\right)=\frac{\sqrt{t-4}}{3t-21}$

Step-by-Step Solution

Answer

The domain of the given function is $\left\{t\right|t\ge 4,t\ne 7\}$

Step 1. Given Information

In the given problems we have to find the domain of given function.

$P\left(t\right)=\frac{\sqrt{t-4}}{3t-21}$

Step 2. The function P tells us to take the square root of t - 4 and divide this result by 3 t - 21 .

This requires that 

$t-4\ge 0$

Add 4 on both side

$$\begin{gathered} t-4+4\ge 0+4 \\ t\ge 4 \end{gathered}$$

and 

$3t-21=0$

Add 21 on both side

$$\begin{gathered} 3t-21+21\ne 0+21 \\ 3t\ne 21 \\ \frac{3}{3}t\ne \frac{21}{3} \\ t\ne 7 \end{gathered}$$

Step 3. Combining these two restrictions,

The domain of P is 

$\left\{t\right|t\ge 4,t\ne 7\}$