Answer:
2x + 1 is defined for all real values
1/(2x + 1) is definded for all real values except x = -1/2
Explanation:
The expression is defined if we can replace the value of x and get a result.
So, for the expression 2x + 1, we can replace x by any value, and we will get a result. For example if x = 10, we get:
2x + 1 = 2(10) + 1 = 21
Or if x = -8.5
2x + 1 = 2(-8.5) + 1 = -16
However, in the second expression is not possible to find a result when we divide by 0. So, when the denominator is equal to 0, the expression is undefined. Then:
[tex]\begin{gathered} 2x+1=0 \\ 2x+1-1=0-1 \\ 2x=-1 \\ \frac{2x}{2}=\frac{-1}{2} \\ x=\frac{-1}{2} \end{gathered}[/tex]Therefore, the second expression is undefined when x = -1/2
Then, the answers are:
2x + 1 is defined for all real values
1/(2x + 1) is definded for all real values except x = -1/2
