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Question 488247: If we choose x from the set of values bigger than 0, is y = x² a function of x? explain
If we choose y from the set of values bigger than 0, is y = x² a function of y? explain
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! y = x^2 makes y a function of x.
the independent variable is x and the dependent variable is y.
x^2 = y makes x^2 a function of y.
the independent variable is y and the dependent variable is x^2.
if we let z = x^2, then:
x^2 = y becomes z = y
z is considered a function of y because it depends on the value of y.
you would solve this like you would solve any equation.
if y = 5, then z = 5
since z = x^2, this means that x^2 = 5.
suppose you had:
x^2 = y-3
x^2 is still a function of y because it depends on the value of y.
if y = 5, x^2 = y - 3 = 5 - 3 = 2
you get x^2 = 2 when y = 5
i believe this to be true, but i won't swear to it.
there may be some rule that says you can't do this, but i haven't seen it.
in practice, you can set anything equal to anything else.
the dependent variable is a function of the independent variable.
the equation determines the value of the dependent variable based on the value of the independent variable.
x^2 is a function of y meets that definition.
the value of x^2 is dependent on the value of y.
the right side of that equation doesn't have to be just y.
it can be any expression involving y.
x^2 = y^3 + 5y - 3 would be an example.
x^2 is a function of y.
when y = 3, x^3 = 27 + 15 - 3 which becomes:
x^2 = 39
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