Problem 6 - Precalculus Essentials

Question

Find the domain of each function. $$f(x)=x^{2}+x-12$$

Step-by-Step Solution

Answer

The domain of the function \(f(x) = x^2 + x - 12\) is all real numbers.

Step 1: Understanding Domain

In mathematics, the domain of a function is the set of all 'input' or argument values for which the function is defined. In simple words, it is the set of all possible x-values which will make the function 'work', and will output real y-values.

Step 2: Identify the type of function

The function \(f(x) = x^2 + x - 12\) is a quadratic function, which is a second order polynomial function without any restrictions to the x-values.

Step 3: Identify the domain of the function

Since there are no square roots, fractions, or logarithms restrictions, we can insert any real number into the function and obtain a real number out. So, the domain of the function is all real numbers.