For diamonds of impeccable quality, the cost C, in dollars, is related to the mass, m, in carats, by the formula

Jay-Z bought an 18-carat engagement ring for Beyoncé at the price of 5 million US dollars. How much are the diamonds in the engagement ring worth?

Example

7716

Cm

Restrictions of Expressions

What would happen if we tried to evaluate the expression for y = 5?

y

y

5

2 5 25 5 0

3

This expression is undefined!

Restrictions of Expressions

Find any real numbers that make the following expression undefined.

4515

49 3

x

xx

The expression is undefined when 15x + 45 = 0.

So the expression is undefined when x = 3.

Example

Find any real numbers that make the following expression undefined

The expression is undefined when 3t +1< 0

So the expression is undefined when t < -1 3

Example

3-t13t

3t +1< 03t < -1t < -1 3

For what values of x is the following expression defined?

The expression is undefined when < 0 and

x + 2 = 0

So the expression is defined when x ≥ 1

Example

< 0 x - 1 < 0x < 1

2

1

x

x

2

1

x

x

2

1

x

x

x + 2 < 0x < -2

Example

dk

49

5 2

Solve the equation for k and determine if any restrictions exist for

Examplea) Solve the equation for f b) Determine if any restrictions exist for the variable t

43.1

1

ft