Find the domain and list all restricted values sqrt 1 - 3x

Question

Find the Domain and list all restricted values sqrt 1 - 3x

Answer 1

As Will R. said the radicand, the part under the

square root sign, must be greater than or equal to zero

 

1-3x ≥ 0

subtract 1 from both sides

-3x ≥ -1

Divide both sides by -3...

Note, when multiply or divide both sides of an inequality

by a negative number it reverses the inequality.

x ≤ 1/3

 

The domain is from negative infinity to 1/3 ... Not -1/3

D = (-∞, 1/3]

Answer 2

Since square roots cannot have a negative number inside them, we will want to find out when inside the square root will become 0 (the minimum amount before the graph would end) and then which way the graph will continue.

 

We will set the inside of the square root equal to 0 and solve for x:     1-3x=0

 

We will next subtract 1 from both sides:     -3x=-1

 

Now we will divide by -3:     x=1/3

 

Since x is being multiplied by a negative number, that means the graph will continue to the left, meaning x can get smaller than 1/3, but not bigger.

 

The domain is (-infinity, 1/3]