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Chapter 2: Q. 7 (page 100)

True or FalseThe cube root function is odd and is decreasing on the interval (-鈭�,鈭�).

Short Answer

Expert verified

The statement 'The cube root function is odd and is decreasing on the interval (-鈭�,鈭�).' is false.

Step by step solution

01

Step 1. Given information

We have been given a statement 'The cube root function is odd and is decreasing on the interval (-鈭�,鈭�).'

We have to tell whether this statement is true or false.

02

Step 2. Check for the odd function 

The cube function is f(x)=x3.

Find f(-x).

f(-x)=-x3

Since, f(-x)isnotequalto-f(x).

This is not an odd function.

03

Step 3. Analyze the graph of cube root function

The graph of cube root function is:

It is clear from the graph that the cube function is increasing everywhere.

Therefore, the given statement is false.

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Most popular questions from this chapter

The function f(x)=x2 is decreasing on the interval _____.

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