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Chapter 2: Q. 6 (page 100)

True or False The cube function is odd and is increasing on the interval (-鈭�,鈭�).

Short Answer

Expert verified

The statement 'The cube function is odd and is increasing on the interval (-鈭�,鈭�).' is true.

Step by step solution

01

Step 1. Given information

We have been given a statement 'The cube function is odd and is increasing 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)=(-x)3 f(-x)=-x3f(-x)=-f(x)

Therefore, the function is odd.

03

Step 3. Analyze the graph of cube function

The graph of cube function is:

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

Therefore, the given statement is true.

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