Question
Find the domain of the function. \( f(x)=x^{2}-10 x-4 \) The domain of \( f(x) \) is \( \square \).
Ask by Wells Lane. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The domain of \( f(x) \) is all real numbers.
Solution
f(x) = x² - 10x - 4 is a polynomial function, and polynomial functions are defined for every real number. Therefore, the domain of f(x) is all real numbers.
The domain of f(x) is (-∞, ∞).
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Simplify this solution Bonus Knowledge
The function \( f(x) = x^{2} - 10x - 4 \) is a polynomial, and the beauty of polynomials is that they are defined for all real numbers. So, if you were wondering about any pesky restrictions like division by zero or square roots of negatives, fear not! The domain of \( f(x) \) is all real numbers, which we can express in interval notation as \( (-\infty, \infty) \). Now, to think of it practically, this means if you were to graph this function, you could plug in any real number you like for \( x \), and it would give you a corresponding \( y \) value. So go ahead—choose your favorite numbers and see how this quadratic behaves!
