no
The function is f(x, y) = x/y where x, y are real, and y ≠0
A Function. That is the definition of a function. I like to think of a function, f(x) as a number crunching machine. the number crunching machine eats different x 's. It eats each and every x and crunches it the same way, but spits out a new Y every time. Remember, y = f(x). That is, "y is a function of x". There you go.
You have Y and you have X. F=function. Y is already a function of X because here's another way you write Y: F(X). So instead of putting Y you out F(X) which meanf "F or X" or "function of X".
The inverse of a function is its reflection in the line y=x. so the only function that returns its own inverse is the line y=x or any part of the line y=x
If what is meant is that the exercise asks whether or not y is a function of x, then it can be determined by a brief experiment with the numbers and variables presented in the equation written. If y is isolated from x depending on the organization of whichever total side of the equation where both variables are written, then it becomes simpler to find whether or not y is a function of x. For example, if the equation is written y2 = x + 4, then y is a function of x because x and y are isolated to different sides of the equation. But if the equation is written, for instance, as y2 + 5x = 4, then y is not a function of x because x and y are not isolated to different sides of the given equation. Furthermore, this rule does not depend upon fractions or estimations. The rule holds true because y is a function of x if x and y are related according to the format of the whole equation and the numbers it contains.
Yes, depending on the function. For example, in the function y = x squared, for x-values of both 2 and -2 you get the same y-value.
The function is f(x, y) = x/y where x, y are real, and y ≠0
A Function. That is the definition of a function. I like to think of a function, f(x) as a number crunching machine. the number crunching machine eats different x 's. It eats each and every x and crunches it the same way, but spits out a new Y every time. Remember, y = f(x). That is, "y is a function of x". There you go.
y = x This is a line and a function. Function values are y values.
You have Y and you have X. F=function. Y is already a function of X because here's another way you write Y: F(X). So instead of putting Y you out F(X) which meanf "F or X" or "function of X".
A binary function is a function f if there exists sets X, Y, and Z, such that f:X x Y -> Z where X x Y is the cartesian product of X and Y.
implicit function/? an equation the function(x,y)=0 defines y implicitly as a function of x the domain of that implicitiy defines function consists of those x for which there is a unique y such that the function (x,y)=0
The inverse of a function is its reflection in the line y=x. so the only function that returns its own inverse is the line y=x or any part of the line y=x
If what is meant is that the exercise asks whether or not y is a function of x, then it can be determined by a brief experiment with the numbers and variables presented in the equation written. If y is isolated from x depending on the organization of whichever total side of the equation where both variables are written, then it becomes simpler to find whether or not y is a function of x. For example, if the equation is written y2 = x + 4, then y is a function of x because x and y are isolated to different sides of the equation. But if the equation is written, for instance, as y2 + 5x = 4, then y is not a function of x because x and y are not isolated to different sides of the given equation. Furthermore, this rule does not depend upon fractions or estimations. The rule holds true because y is a function of x if x and y are related according to the format of the whole equation and the numbers it contains.
Either - or both - can be true.
y2 + x = 7 : this can be written as y2 = 7 - x or x = 7 - y2. There is not a specific solution to this identity. For each different value assigned to x then a different value is generated for y. Or, it can be viewed that for each different value assigned to y then a different value is generated for x. This expression is therefore a function.
Both. If you look at it like this: y=41-x you say x is independent and y is dependent of x (i.e. y is a function of x) For x=41-y you say y is independent and x is dependent of y (i.e. x is a function of y)