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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 559RE (page 855)

In the following exercises, find the domain of the function and write the domain in interval notation.
$F (x) = \sqrt[4]{10 - 7 x}$

Short Answer

Expert verified

Domain is $x \in (- \infty, \frac{10}{7}]$

Step by step solution

01

Given information

Domain of $F (x) = \sqrt[4]{10 - 7 x}$

02

Solution

We have

$F (x) = \sqrt[4]{10 - 7 x}$

Here the we need to find fourth root

For fourth root value inside should be positive

Hence

$10 - 7 x \geq 0 7 x \leq 10 x \leq \frac{10}{7} x \in (- \infty, \frac{10}{7}]$

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Most popular questions from this chapter

Simplify:

$(a) \sqrt{\frac{98}{162}} (b) \sqrt[3]{\frac{24}{375}} (c) \sqrt[4]{\frac{4}{324}}$

Use the Quotient Property to simplify square roots.

(a) $\frac{\sqrt{80 q^{5}}}{\sqrt{5 q}}$

(b) $\frac{\sqrt[3]{- 625}}{\sqrt[3]{5}}$

(c) $\frac{\sqrt[4]{80 m^{7}}}{\sqrt[4]{5 m}}$

In the following exercises, solve.
$\sqrt{v - 10} + 10 = v$

Use the Quotient Property to simplify square roots.

(a) $\frac{\sqrt{45 p^{9}}}{\sqrt{5 q^{2}}}$

(b) $\frac{\sqrt[4]{64}}{\sqrt[4]{2}}$

(c) $\frac{\sqrt[5]{128 x^{8}}}{\sqrt[5]{2 x^{2}}}$

In the following exercises, write with a rational exponent.

$ⓐ \sqrt[7]{x} ⓑ \sqrt[9]{y} ⓒ \sqrt[5]{f}$

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