Find the domain of the function: f (x) = 1+4x / 2x − 1

Question

Find the domain of the function

Answer 1

Hello Briana,

For a rational function such as this, the domain will be any value except for those which make the denominator zero.

 

So, setting the denominator of

2x - 1 = 0, we get

x = 1/2, which we don't want.

 

Then, depending on the teacher, there are several ways you can write your final answer.

 

Domain:

x ≠ 1/2 (not a very precise form, but...)

All Reals except x = 1/2

ℜ - {1/2}

{x | x ∈ ℜ and x ≠ 1/2}

(-inf , 1/2) ∪ (1/2, inf)

Answer 2

Assuming you mean:

f (x) = (1+4x) / (2x − 1)          always use grouping symbols!!

 

ℜ - {0.5}