ANSWER:
(a)
A. The domain of the given function is {yly is a real number, y ≠ 1}
(b)
[tex]\begin{equation*} D=\left(-\infty\:,\:1\right)\cup\left(1,\:\infty\:\right) \end{equation*}[/tex]
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f(y)=\frac{y}{y-1}[/tex]
The domain of a function, are the input values of the function, in this case, it corresponds to the values that y can take.
Since it is a rational function and it cannot take values that make the denominator zero, so we set the denominator equal to zero, like this:
[tex]\begin{gathered} y-1=0 \\ \\ y\ne1 \end{gathered}[/tex]
(a)
That means that y can take the value of all reals except 1.
So the correct answer is:
A. The domain of the given function is {yly is a real number, y ≠ 1}
(b)
In its interval form it would be:
[tex]D=\left(-\infty\:,\:1\right)\cup\left(1,\:\infty\:\right)[/tex]
