Does the domain of odd and even functions have to be R?
Generally, yes, but it’s not a hard and fast rule (not if it’s defined in the textbook). There’s no harm in treating 1/x as an odd function, just be aware that it’s not defined at the 0 point. Of course the domain of definition must be symmetric about the origin, this is the definition of a parity function.
Is the domain of definition of the function discriminant to find the value domain X necessarily R
① if f (x) is an integer, then the domain of definition of the function is the set of real numbers R;
② if f (x) is a fractional equation, then the domain of definition of the function is the set of real numbers such that the denominator is not equal to 0;
③ if f (x) is a quadratic equation, then the domain of definition of the function is the set of real numbers such that the equation in the root sign is greater than or equal to 0 set;
④ if f (x) is a mathematical equation consisting of several parts, the domain of definition of the function is the set of real numbers that makes each part of the equation meaningful;
⑤ if f (x) is a function abstracted from a real problem, the domain of definition of the function should match the real problem.
Is the domain of a periodic function always R
The definition of a periodic function is embodied in the period, and is not related to the domain of the function, which can be R, or any other domain.
Exponential function domain
Exponential function domain is R. Here the premise is a greater than 0 and not equal to 1. For a not greater than 0, the function must make the definition of the domain of the discontinuous, so we do not take into account, and at the same time, a is equal to the function of the meaninglessness of the function of 0 is generally not taken into account.
Exponential function is one of the important basic elementary functions. In general, y = a function (a is a constant and to a & gt; 0, a ≠ 1) is called the exponential function, the function of the definition of the domain is R. In the definition of the exponential function of the expression, the coefficient in front of a must be the number of 1, the independent variable x must be in the position of the exponent, and can not be any other expression of x. Otherwise, it is not an exponential function.
Exponential function has an obvious law, is when a from 0 tends to infinity in the process (not equal to 0) function of the curve from the position of monotonous decreasing function, respectively, close to the positive half-axis of the y-axis and the x-axis, tends to be close to the positive half-axis of the y-axis and the negative half-axis of the x-axis of the monotonous increasing function, respectively, the position. Where the horizontal line y = 1 is a transition position from decreasing to increasing. When the index is negative, generally first inverted bottom, that is, first the bottom number into the inverse and the index of the superwill its opposite.
How to determine whether the definition domain of a function is R?
You can be regarded as limiting the function value domain of the range of the value of the self-contained variable, such as a primary function y = 2x + 1, for x, there is no restriction so the definition domain of this function for R, but if the inverse function y = 1/x this, because the denominator of the fraction can not be zero, so the definition of the function of the domain of the position of the (0, + ∞).
Function definition domain: mathematical term, is one of the three elements of the function (definition domain, value domain, corresponding to the law), corresponding to the object of the law. Refers to the range of values of the function’s independent variable, that is, for two non-empty sets D, M that have a functional correspondence, any number in the set D, there is and only a definite number in the set M with which it corresponds, then the set D is called the domain of definition of the function.