Find the Domain f(x)*(10x^4)-4x^3-8x^2+3x-6

Problem

ƒ(x)=10*x4−4*x3−8*x2+3*x−6

Solution

1. Identify the type of function. The given expression ƒ(x)=10*x4−4*x3−8*x2+3*x−6 is a polynomial function.

2. Determine potential restrictions. Polynomial functions do not contain variables in denominators, under even-indexed radicals, or within logarithms.

3. Apply the domain rule for polynomials. Since there are no values of x that result in division by zero or non-real numbers, the function is defined for all real numbers.

4. Express the domain in interval notation. The set of all real numbers is represented as (−∞,∞)

Final Answer

Domain: *(−∞,∞)

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