# The values of x for the expression 6 x − x 2 , where x is defined as real number. ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1, Problem 13T
To determine

## To find: The values of x for the expression 6x−x2, where x is defined as real number.

Expert Solution

The values of x in 0x6 defined as a real numbers.

### Explanation of Solution

The expression is 6xx2.

The expression 6xx2 is defined as a real number when polynomial function 6xx2 is greater than or equal to zero.

The square roots of any function is not defined for negative values of function.

Thus,

6xx20

On further simplification,

x(6x)0

The factors of the left-hand side are x, (6x) and these are zero when x=0,6.

Two possible values of x give the corresponding intervals of inequality (,0), (0,6) and (6,).

Now, make a table indicating the sign of each factor on each interval,

 x<0 x=0 06 x − 0 + + + (6−x) + + + 0 − x(6−x) − 0 + 0 −

Table (1)

From the above sign table, the inequality is satisfied on the intervals (0,6) and the end points of intervals x=0 and x=6.

So the solution of given expression is all x-values, in between x=0 to x=6, for which the expression 6xx2 is defined as a real number.

Thus, the values of x in 0x6 defined as a real numbers.

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!