# Definitional Domain of a Function and Function Value Questions

### Just learning functions, there is a question about the definition domain and value domain of the function would like to ask

f (x) has the definition domain of [0,1], what is in () is the independent variable, the definition domain is [0,1], which means that 0 ≤ x ≤ 1;

When the function is f (x + 2), the independent variable in () is x + 2 now, but the definition domain is still [0, 1], so There is 0 ≤ x+2 ≤ 1, and solving it gives -2 ≤ x ≤ -1.

### About the function value domain definition domain problem

First of all, your statement is problematic, what is the function of the domain, like Y = aX^2 + bX + c (a, b, c is a constant), the range of values of Y is the function of the domain, Y ≠ 0, how can it be R, R contains 0, if Y = 0, then it is 0. The test will not be like this.

Why is the domain of a function R when Y ≠ 0?

That’s still a problem, if Y=0 and x has a solution, then its domain is X≠X1 (the solution of x) X belongs to R

Fix it again, I don’t know what you’re asking.

### Function of the definition of the domain and the value of the domain

Function of the definition of the domain and the value of the domain is: the range of values of the independent variable is called the function of the definition of the domain, the set of values of the function is called the function of the domain of the value of the function.

The common methods to find the definition domain of a function are

(1) according to the analytic requirements such as even radicals of the equation is greater than zero, the denominator can not be zero, etc.;

(2) according to the requirements of the actual problem to determine the range of the independent variable;

(3) according to the definition domain of the relevant analytic to determine the range of the independent variable of the function being sought;

(4) Definition domain of composite function: if y is a function of u and u is a function of x, i.e., y=f(u), u=g(x), then y=f[g(x)] is called a composite function of the functions f and g, and u is called an intermediate variable, let the definition domain of f(x) be x∈M, and that of g(x) be x∈N, and to find the definition domain of y=f[g(x)], then it is only necessary to satisfy

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the set of x’s. Let the domain of definition of y=f[g(x)] be P. Then

Common function value domains

1. y=kx+ (k≠0) has value domain R

2. y=k/x has value domain (-∞,0)∪(0,+∞)

3. y=√x has value domain x≥0

4. y=ax^2+bx+c when a& gt;0, the domain of value is [4ac-b^2/4a,+∞)

5, when a<0, the domain of value is (-∞, 4ac-b^2/4a]

6, y=a^x has the domain of value (0,+∞)

7, y=lgx has the domain of value R