a)
x+y2=14
⟹y2=14−x
⟹y=±14−x−−−−−√
Let’s say we plug in x=5
, we will get y=±3
The definition of a function says that one input must give us at most one output. This tells us that from this equation we cannot have y
as a function of x
.
b)
x3−y3=27
⟹y3=x3−27
⟹y=x3–27−−−−−√3
The cube root function gives us one output per input. As a consequence of the previous statement and using the definition of function we can say that from this equation we can write y
as a function of x
.