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Chapter 1: Problem 30

Determine the domain of the function represented by the given equation. $$f(x)=3 x^{2}+1$$

Short Answer

Expert verified
The domain of the function \(f(x)=3 x^{2}+1\) is all real numbers, or in interval notation, \(-\infty, \infty\).

Step by step solution

01

Identify the function type

The function can be identified as a quadratic function expressed in the form \(f(x) = ax^{2} + b\). Its graph would be a parabola.
02

Determine any restrictions

The function does not contain any fractions with \(x\) as the denominator (which might cause division by zero), or any root or logarithmic operations that might impose restrictions on \(x\). Therefore, there are no restrictions on the x-values.
03

State the domain

Since there are no restrictions to the x-values, the domain is the set of all real numbers. This can be written in interval notation as \(-\infty, \infty\).

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Most popular questions from this chapter

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