Question

True or false

If an original expression is defined for all values of x, you do not need to specify the absolute value in the simplified expression

Answer 1

The given statement is FALSE.

Explanation:

If the original expression is defined for all values of x , then this implies there is no real value of x such that the original expression is not defined.

Hence, the original expression has domain all real values x

Now, the simplified form which is obtained by simplifying the original expression may not have the same domain as the original expression.

So, if original expression is defined on some value of x then it might be possible that the simplified expression may not be defined on that value of x.

So, we need to specify the absolute value in the simplified expression.

Hence the given statement is FALSE.