Chapter 11: Q. 557RE (page 1069)

In the following exercises, find the domain of the function and write the domain in interval notation.
$F (x) = \sqrt{\frac{x + 3}{x - 2}}$

Short Answer

Expert verified

Domain is $x \in (- \infty, - 3] \cup (2, \infty)$

Step by step solution

Given information

Domain of $F (x) = \sqrt{\frac{x + 3}{x - 2}}$

Solution

We have

$F (x) = \sqrt{\frac{x + 3}{x - 2}}$

Here

$\frac{x + 3}{x - 2} \geq 0$

Taking the intervals
$(- \infty, - 3], (- 3, 2], (2, \infty)$

Checking

In localid="1663766527461" $(- \infty, - 3]$ value of $\frac{x + 3}{x - 2} \geq 0$

In localid="1663766706310" $(- 3, 2]$ value of localid="1663766578080" $\frac{x + 3}{x - 2} < 0$ is not defined or negative

In localid="1663766538327" $(2, \infty)$ value of $\frac{x + 3}{x - 2} \geq 0$

Hence the domain is

$x \in (- \infty, - 3] \cup (2, \infty)$

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In the following exercises, find the domain of the function and write the domain in interval notation.
$F (x) = \sqrt{\frac{x + 3}{x - 2}}$

Short Answer

Step by step solution

Given information

Solution

One App. One Place for Learning.

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In the following exercises, find the domain of the function and write the domain in interval notation.F(x)=x+3x-2

Short Answer

Step by step solution

Given information

Solution

One App. One Place for Learning.

Most popular questions from this chapter

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In the following exercises, find the domain of the function and write the domain in interval notation.
$F (x) = \sqrt{\frac{x + 3}{x - 2}}$