Math exercise

Question

 

Find the domain of: f(x)=√3-2x

Answer 1

If all of 3-2x is under the square root, any value that would cause the radicand (the value under the radical) to become a negative number is imaginary. So you need to find the value for which 3-2x would become zero by setting it equal to zero.

 

3-2x = 0

-3      -3

 

-2x = -3

÷ -2   ÷ -2

 

x = 3/2 = 1.5

 

This value would cause the radicand to become zero. Now you have to decide whether you can plug in values greater than 1.5 or less than 1.5.

 

Test the value 2:  3 - 2(2) = 3 - 4 = -1

 

You can't use a value greater than 1.5 because your radicand becomes negative.

 

Test the value 1:  3 - 2(1) = 3 - 2 = 1

 

You can have positive values in the square root. Any value you test when x is less than 1.5 will work.

 

Your domain is all reals less than or equal to 1.5.   x ≤ 1.5

Answer 2

The domain of a function is the set of all values of x for which f(x) is defined.  

 

If f(x) = √(3-2x), then f(x) is a real number only when 3 - 2x ≥ 0

 

                                                                                                     -2x ≥ -3

 

                                                                                                         x ≤ 3/2

 

Domain {x l x ≤ 3/2} = (-∞, 3/2]