Chapter 2: Q. 61 (page 69)

In Problems 47– 62, find the domain of each function.
$P (t) = \frac{\sqrt{t - 4}}{3 t - 21}$

Short Answer

Expert verified

The domain of the given function is ${t | t \geq 4, t \neq 7}$

Step by step solution

Step 1. Given Information

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

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

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

This requires that

$t - 4 \geq 0$

Add 4 on both side

role="math" localid="1646019797420" $t - 4 + 4 \geq 0 + 4 t \geq 4$

and

$3 t - 21 = 0$

Add 21 on both side

role="math" localid="1646019936386" $3 t - 21 + 21 \neq 0 + 21 3 t \neq 21 \frac{3}{3} t \neq \frac{21}{3} t \neq 7$

Step 3. Combining these two restrictions,

The domain of P is

${t | t \geq 4, t \neq 7}$

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In Problems 47– 62, find the domain of each function.
$P (t) = \frac{\sqrt{t - 4}}{3 t - 21}$

Short Answer

Step by step solution

Step 1. Given Information

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

Step 3. Combining these two restrictions,

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In Problems 47– 62, find the domain of each function.P(t)=t-43t-21

Short Answer

Step by step solution

Step 1. Given Information

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

Step 3. Combining these two restrictions,

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

In Problems 47– 62, find the domain of each function.
$P (t) = \frac{\sqrt{t - 4}}{3 t - 21}$