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The domain of a function encompasses all of the possible inputs of that function. On a Cartesian graph, this would be the x axis. For example, the function y = 2x has a domain of all values of x. The function y = x/2x has a domain of all values except zero, because 2 times zero is zero, which makes the function unsolvable.
x is a letter often used as a variable. It can be in the range or the domain. However, in elementary algebra, the variable x is most often used for the domain and f(x) =y for the range.
Assuming the standard x and y axes, the range is the maximum value of y minus minimum value of y; and the domain is the maximum value of x minus minimum value of x.
Quite simply, the domain is the input and the range is the output of a function. If your using a typical X-Y axis graph, it may be useful to view the X axis as where the domain lies. The Y axis is where the range lies. Y= f(x) or Range = f(domain)
y=S^5x _cos(x) cos(u²) du The derivative of a definite integral of a function f(x) is equal to the difference in the product of the function at each limit of integration times the limit of integration. y'=cos(u²)*du/dx from u=cos(x) to u=5x y'=-sin(x)*cos(cos(x)²)-5*cos(25x²) To understand why this works, consider the following where F(x) is the antiderivative of f(x) y=F(g(x))-F(h(x))=S f(x)dx from h(x) to g(x) If you take the derivative of this expression and apply the chain rule dy/dx = dF(g(x))/dx - dF(h(x))/dx = f(g(x))*dg/dx - f(h(x))*dh/dx