Answer:
The equation can define y as a function of x and it also can define x as a function of y.
Step-by-step explanation:
A relation is a function if and only if each value in the domain is mapped into only one value in the range.
So, if we have:
f(x₀) = A
and, for the same input x₀:
f(x₀) = B
Then this is not a function, because it is mapping the element x₀ into two different outputs.
Now we want to see it:
x + y = 27
defines y as a function of x.
if we isolate y, we get:
y = f(x) = 27 - x
Now, this is a linear equation, so for each value of x we will find an unique correspondent value of y, so yes, this is a function.
Now we also want to check if:
x + y = 27
defines x as a function of y.
So now we need to isolate x to get:
x = f(y) = 27 - y
Again, this is a linear equation, there are no values of y such that f(y) has two different values. Then this is a function.
