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Answer :
To find the domain of the function [tex]\( f(x) = 15x^4 + 6x^3 - 3x^2 - 2x + 19 \)[/tex], we need to determine the set of all possible values of [tex]\( x \)[/tex] that can be used in the function without causing any mathematical issues, like division by zero or taking the square root of a negative number.
Let's break it down:
1. Identify the Function Type: The function given is a polynomial. Polynomial functions are expressions that involve only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
2. Consider Characteristics of Polynomial Functions: A key characteristic of polynomial functions is that they are defined for all real numbers. This means there are no restrictions on the input values (i.e., the domain).
3. State the Domain: Since polynomials do not have denominators or radicals that could limit the input values, the domain of [tex]\( f(x) = 15x^4 + 6x^3 - 3x^2 - 2x + 19 \)[/tex] is all real numbers. There's nothing in the expression that could cause division by zero or issues with undefined values.
Therefore, the domain of the function [tex]\( f(x) \)[/tex] is all real numbers. You can input any real number into this function, and it will produce a real number as output.
Let's break it down:
1. Identify the Function Type: The function given is a polynomial. Polynomial functions are expressions that involve only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
2. Consider Characteristics of Polynomial Functions: A key characteristic of polynomial functions is that they are defined for all real numbers. This means there are no restrictions on the input values (i.e., the domain).
3. State the Domain: Since polynomials do not have denominators or radicals that could limit the input values, the domain of [tex]\( f(x) = 15x^4 + 6x^3 - 3x^2 - 2x + 19 \)[/tex] is all real numbers. There's nothing in the expression that could cause division by zero or issues with undefined values.
Therefore, the domain of the function [tex]\( f(x) \)[/tex] is all real numbers. You can input any real number into this function, and it will produce a real number as output.
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