Chapter 4: Q. 70 (page 242)

What is the domain of the function $f (x) = \sqrt{x^{3} - 3 x^{2}} ?$

Short Answer

Expert verified

The domain of the function is a set of all real numbers greater than or equal to $3 .$

Step by step solution

Step 1. Given Information

The given function is $f (x) = \sqrt{x^{3} - 3 x^{2}}$

We have to find the domain.

Step 2. Finding the domain

As the given function is a square root function.

To find the domain first, find the real zeros of f(x).

So, $\sqrt{x^{3} - 3 x^{2}} = 0 x^{3} - 3 x^{2} = 0 x^{2} (x - 3) = 0 x^{2} = 0 a n d x - 3 = 0 x = 0 x = 3$

Step 3. Determining intervals

Now, by using the real zeros the intervals we get are

$(- \infty, 0), (0, 3), (3, \infty) .$

Step 4. Check the points

Let $x = - 2$ and substitute in the given function

$f (- 2) = \sqrt{{(- 2)}^{3} - 3 {(- 2)}^{2}} = \sqrt{- 8 - 12} = \sqrt{- 20}$

So, it is not true.

Let $x = 2$ and substitute in the given function

$f (2) = \sqrt{{(2)}^{3} - 3 {(2)}^{2}} = \sqrt{8 - 12} = \sqrt{- 4}$

So, it is not true.

Let $x = 4$ and substitute in the given function

$f (4) = \sqrt{{(4)}^{3} - 3 {(4)}^{2}} = \sqrt{64 - 48} = \sqrt{16} = 4$

So, it is true.

Therefore, the domain of the function is all real numbers greater than or equal to $3 .$

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What is the domain of the function $f (x) = \sqrt{x^{3} - 3 x^{2}} ?$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the domain

Step 3. Determining intervals

Step 4. Check the points

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What is the domain of the functionf(x)=x3-3x2?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the domain

Step 3. Determining intervals

Step 4. Check the points

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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What is the domain of the function $f (x) = \sqrt{x^{3} - 3 x^{2}} ?$