Chapter 2: Q. 10 (page 124)

Find the domain of each function.
$f (x) = \frac{\sqrt{x + 1}}{x^{2} - 4}$

Short Answer

Expert verified

The domain of the function $f (x) = \frac{\sqrt{x + 1}}{x^{2} - 4}$ is role="math" localid="1645963482579" ${x | x \geq - 1; x \neq 2}$ .

Step by step solution

Step 1. Given information

We have been given a function $f (x) = \frac{\sqrt{x + 1}}{x^{2} - 4}$ .

We have to find its domain.

Step 2. Find the values that make the square root function undefined

Square root function is defined for nonnegative numbers.

Therefore, $(x + 1)$ should be non-negative.

$x + 1 \geq 0 x + 1 - 1 \geq 0 - 1 (Subtract 1 from both sides) x \geq - 1$

Step 3. Find the values where the denominator becomes zero

The given function will not be defined where the denominator becomes zero.

We need to exclude those values of $x$ .

$x^{2} - 4 = 0 x^{2} - 4 + 4 = 0 + 4 (Add 4 on both sides) x^{2} = 4 x = \pm \sqrt{4} (Take square roots on both sides) x = \pm 2$

Therefore, the domain will be ${x | x \geq - 1; x \neq 2}$ .

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Find the domain of each function.
$f (x) = \frac{\sqrt{x + 1}}{x^{2} - 4}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the values that make the square root function undefined

Step 3. Find the values where the denominator becomes zero

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Find the domain of each function.f(x)=x+1x2-4

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the values that make the square root function undefined

Step 3. Find the values where the denominator becomes zero

One App. One Place for Learning.

Most popular questions from this chapter

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Find the domain of each function.
$f (x) = \frac{\sqrt{x + 1}}{x^{2} - 4}$