Chapter 4: Q. 69 (page 242)

What is the domain of the function $f (x) = \sqrt{x^{4} - 16}$ ?

Short Answer

Expert verified

The domain of the function is ${x | x \leq - 4 o r x \geq 4}$ and the interval notation is $(- \infty, - 4] \cup [4, \infty) .$

Step by step solution

Step 1. Given Information

The given function is $f (x) = \sqrt{x^{4} - 16}$

We have to find the domain.

Step 2. Finding the domain

As the given function is a square root function.

To find the domain of a square root function, set the radicand to greater than or equal to zero.

So,

$x^{4} - 16 \geq 0 (x^{2} - 4) (x^{2} + 4) \geq 0$

Step 3. Check the points

Let $x = - 6$ and substitute in $(x^{2} + 4) (x^{2} - 4) \geq 0$

$({(- 6)}^{2} + 4) ({(- 6)}^{2} - 4) \geq 0 (40) (32) \geq 0$

So, it is true.

Let $x = 0$ and substitute in $(x^{2} + 4) (x^{2} - 4) \geq 0$

$(0 + 4) (0 - 4) \geq 0 - 16 \geq 0$

So, it is false.

Let $x = 6$ and substitute in $(x^{2} + 4) (x^{2} - 4) \geq 0$

$({(6)}^{2} + 4) ({(6)}^{2} - 4) \geq 0 (40) (32) \geq 0$

So, it is true.

The domain of the function is ${x | x \leq - 4 o r x \geq 4}$ and the interval notation is $(- \infty, - 4] \cup [4, \infty) .$

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What is the domain of the function $f (x) = \sqrt{x^{4} - 16}$ ?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the domain

Step 3. Check the points

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What is the domain of the functionf(x)=x4-16?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the domain

Step 3. Check the points

One App. One Place for Learning.

Most popular questions from this chapter

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What is the domain of the function $f (x) = \sqrt{x^{4} - 16}$ ?