### Instruction: What is the domain of the function $$k(y) = \frac{1}{2y+1}~?$$ Express your answer in interval notation.### Response: To find the domain of a function, I need to identify the values of y that would make the function undefined or invalid.
One thing that can make a function undefined is dividing by zero, so I want to avoid that.
That means I need to exclude any values of y that would make the denominator 2y+1 equal to zero.
To find those values, I can set 2y+1 equal to zero and solve for y.
Subtracting 1 from both sides gives me 2y = -1, and dividing both sides by 2 gives me y = -0.5.
So y = -0.5 is the only value that would make the function undefined.
Therefore, the domain of the function is all real numbers except y = -0.5.
To write this in interval notation, I use parentheses to indicate that y = -0.5 is not included, and I use infinity symbols to indicate that there is no other bound on the domain.
The domain in interval notation is $$(-\infty, -0.5) \cup (-0.5, \infty)$$