How do you see that his domain of definition is R
f(x)
=-x^2;x<0(x<0,f(x) is defined)
=2x+1;x≥0(x≥0,f(x) is defined)
Domain of definition of f(x)=R
How to determine when the function definition domain is R, when it is not, and how to determine the same function, say simple and clear point, the foundation is not good,
General function definition domain restrictions have denominator is not zero, the way to be open is not less than zero, logarithmic function of the truth is greater than zero, etc., according to these restrictions to solve the range of that is the definition of the domain. Need to remember some special function restrictions. The function is the same i.e. the expression of the function is the same, the definition domain is also the same
How to determine whether the function definition domain is R
Power function x^a
If a is negative then it is equivalent to (1/x)^(-a), so X is to do the denominator can’t area 0 is not R
Therefore, a is a negative is not R definition
What is the specific analysis of the statement that if f(x) is an integer, then the domain of definition of the function is the real numbers R?
Monomials and polynomials are collectively referred to as integers, i.e., not fractions, and the domain of a function is the range of values of x that are real numbers, not complex numbers, so the implication should be that if the function is an integer then the domain of definition is the real numbers, whereas if the function is not an integer then its domain of definition is a different matter.
(1) If f(x) is an integer, then the domain of definition of the function is R;
(2) If f(x) is a fraction, then the domain of definition of the function is the set of real numbers such that the denominator is not equal to zero;
(3) If f(x) is a quadratic, then the domain of definition of the function is the set of real numbers such that the number of the open square is not less than zero;
(4) ) If f (x) is a zero power of a number, then the domain of definition of the function is the set of real numbers such that the base is not zero.
Terms:
In a polynomial, each monomial is called a term of the polynomial, and the terms that do not contain letters are called constant terms. A polynomial is called a polynomial with several terms after combining like terms. The symbols in a polynomial are considered as the property symbols of the terms. A monic Nth degree polynomial has at most N+1 terms.
(1) The number of times of a polynomial is the number of times of the highest number of terms, not the sum of the number of times of the terms, the concept should be understood thoroughly.
(2) See whether the arrangement is in descending or ascending powers.
(3) Both descending and ascending power arrangements are ordered by a certain letter (unknown quantity).
How to find the domain of a function
The method of finding the domain of a function is as follows:
1. The domain of an integer is R. The integer can be divided into monomials and polynomials, monomials, such as y = 4x, polynomials, such as y = 4x + 1. In this case, whether it’s a monomial or a polynomial, the domain of the function is ¡× | x ¡× ∈ R¡}, that is, x can be equal to all the real numbers.
2, the definition of the domain of the denominator is not equal to 0. For example, y = 1/(x-1), the definition of the domain of this time only requires that the denominator is not equal to can be, that is, x-1 ≠ 0, the definition of the domain of ｛x | x ≠ 1｝.
3, even the square root of the definition of the number of square ≥ 0. For example, the root of x-3, the definition of the domain is to let x-3 ≥ 0, out of the definition of the domain ｛x | x ≥ 3｝.
4, the definition of the odd square root is R. For example, three times under the root sign x-3, the definition of the domain is ｛x | x ∈ R｝.
5. The exponential function definition domain is R. For example, y = 3^x, the definition domain is ｛x | x ∈ R｝.
6, the logarithmic function definition domain is true > 0. For example, log with 3 as the base (x-1) log, let x-1 > 0, that is, the definition domain is ｛x | x > 1｝.
7, power function definition domain is the base ≠ 0. For example, y = (x-1)^2, let x-1 ≠ 0, that is, the definition domain is ｛x | x ≠ 1｝.
8, trigonometric functions in the sine cosine definition of the domain of R, tangent function definition of the domain of x ≠ π / 2 + k π. This time to find the definition of the domain of the drawing of a diagram can be seen, as long as the trigonometric function image to memorize, you can find the definition of the domain.