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Usually very little.

f(x) simply denotes the function f except that with this notation it is explicit that f(x) is a function of the variable x (and only x).

So, f = x + 3 and f(x) = x + 3 are equivalent.

However, there will be times, with functions of more than one variables where you wish to consider only one of the arguments while holding the other argument constant.

Q: What is the difference in meaning between f and f x?

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Usually none. A function can be identified as f but it is more often denoted by f(x) to show that it is a function of x.

A Maclaurin series is centered about zero, while a Taylor series is centered about any point c. M(x) = [f(0)/0!] + [f'(0)/1!]x +[f''(0)/2!](x^2) + [f'''(0)/3!](x^3) + . . . for f(x). T(x) = [f(c)/0!] + [f'(c)/1!](x-c) +[f''(c)/2!]((x-c)^2) + [f'''(c)/3!]((x-c)^3) + . . . for f(x).

Looks like simple difference formula work here. f(x) - g(x) = f'(x) - g'(x) e - 5x = e - 5 =====

No, they are the inverse functions, while csc, sec and cot are the reciprocal functions. To illustrate the difference, the inverse of f(x) = x+3 is f-1(x) = x-3 But the reciprocal of f(x) is 1/f(x) = 1/(x+3)

( ) is a<x<b, ( ] is a<x<=b, [ ) is a<=x<b, [ ] is a<=x<=b. If there is no [ or solid bracket then there isn't a filled in dot, meaning that that number is not included. There is only a filled in dot when there is a solid bracket.

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Even polynomial functions have f(x) = f(-x). For example, if f(x) = x^2, then f(-x) = (-x)^2 which is x^2. therefore it is even. Odd polynomial functions occur when f(x)= -f(x). For example, f(x) = x^3 + x f(-x) = (-x)^3 + (-x) f(-x) = -x^3 - x f(-x) = -(x^3 + x) Therefore, f(-x) = -f(x) It is odd

Usually none. A function can be identified as f but it is more often denoted by f(x) to show that it is a function of x.

A Maclaurin series is centered about zero, while a Taylor series is centered about any point c. M(x) = [f(0)/0!] + [f'(0)/1!]x +[f''(0)/2!](x^2) + [f'''(0)/3!](x^3) + . . . for f(x). T(x) = [f(c)/0!] + [f'(c)/1!](x-c) +[f''(c)/2!]((x-c)^2) + [f'''(c)/3!]((x-c)^3) + . . . for f(x).

If you mean a number subtracted by 5 then your formula, or linear equation is f(x)=x-5 Meaning if the value x is the input of the function, then the output is x-5. Example: f(17)=17-5=12 So f(17)=12 Make sense?

A power function has the equation f(x)=x^a while an exponential function has the equation f(x)=a^x. In a power function, x is brought to the power of the variable. In an exponential function, the variable is brought to the power x.

the difference between a number and 3 is

The main difference between light and x-rays is that x-rays are radiation.

Given a function f, of a variable x, the roots of the equation are values of x for which f(x) = 0.If the function, f, happens to be a polynomial function, and r is a root of f(x) then (x - r) is a factor of f(x).

15 - x

Looks like simple difference formula work here. f(x) - g(x) = f'(x) - g'(x) e - 5x = e - 5 =====

While no set of rules can handle differentiating every expression, the following should help. For all of the following, assume c and n are constants, f(x) and g(x) are functions of x, and f'(x) and g'(x) mean the derivative of f and g respectively. Constant derivative rule:d/dx(c)=0 Constant multiple rule:d/dx(c*f(x))=c*f'(x) Sum and Difference Rule:d/dx(f(x)±g(x))=f'(x)±g'(x) Power rule:d/dx(xn)=n*xn-1 Product rule:d/dx(f(x)*g(x))=f'(x)*g(x) + g'(x)*f(x) Quotient rule:d/dx(f(x)/g(x))=(f'(x)*g(x)-g'(x)*f(x))/f(x)² Chain rule:d/dx(f(g(x))= f'(g(x))*g'(x)

No, they are the inverse functions, while csc, sec and cot are the reciprocal functions. To illustrate the difference, the inverse of f(x) = x+3 is f-1(x) = x-3 But the reciprocal of f(x) is 1/f(x) = 1/(x+3)