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Answer :
To find the domain of the function [tex]\( f(x) = 7x^{15} + 23x^8 - 38x^6 + 22x^4 + 35x^3 + 10 \)[/tex], follow these steps:
1. Identify the type of function: The given function is a polynomial. Polynomials are sums of terms consisting of a variable (in this case, [tex]\( x \)[/tex]) raised to non-negative integer powers and multiplied by coefficients.
2. Recall the properties of polynomials: Polynomials are defined for all real numbers because you can substitute any real number for [tex]\( x \)[/tex] without any issues such as division by zero or taking the square root of a negative number.
3. State the domain: Since polynomials are defined for all real numbers, the domain of the function [tex]\( f(x) = 7x^{15} + 23x^8 - 38x^6 + 22x^4 + 35x^3 + 10 \)[/tex] consists of all real numbers.
So, the domain of [tex]\( f(x) \)[/tex] is [tex]\(\boxed{\text{all real numbers}}\)[/tex] or in interval notation, [tex]\((-\infty, \infty)\)[/tex].
1. Identify the type of function: The given function is a polynomial. Polynomials are sums of terms consisting of a variable (in this case, [tex]\( x \)[/tex]) raised to non-negative integer powers and multiplied by coefficients.
2. Recall the properties of polynomials: Polynomials are defined for all real numbers because you can substitute any real number for [tex]\( x \)[/tex] without any issues such as division by zero or taking the square root of a negative number.
3. State the domain: Since polynomials are defined for all real numbers, the domain of the function [tex]\( f(x) = 7x^{15} + 23x^8 - 38x^6 + 22x^4 + 35x^3 + 10 \)[/tex] consists of all real numbers.
So, the domain of [tex]\( f(x) \)[/tex] is [tex]\(\boxed{\text{all real numbers}}\)[/tex] or in interval notation, [tex]\((-\infty, \infty)\)[/tex].
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