To find the domain of the function F(x) = 4x² − 1: Step 1: Identify the type of function. The function F(x) = 4x² − 1 is a polynomial function. Step 2: Determine restrictions on the input variable x. Polynomial functions are defined for all real numbers. There are no square roots of negative numbers, no denominators that could be zero, and no logarithms of non-positive numbers. Therefore, there are no restrictions on the values x can take. Step 3: State the domain. The domain of the function is all real numbers. In set-builder notation: x x ∈ R In interval notation: (−∞, ∞)

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F(x) = 4x² − 1

October 12, 2026Mathematics

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Answer

\left\{x \mid x \in \mathbb{R}\right\}

\left(-\infty, \infty\right)

Graph of F(x) = 4x² − 1

Key points of F(x) = 4x² − 1
Point	x	y
x-intercept	−0.5	0
Minimum	0	−1
x-intercept	0.5	0

Step-by-step solution

3 steps

To find the domain of the function $F(x) = 4x^2 - 1$ :

Identify the type of function.
The function $F(x) = 4x^2 - 1$ is a polynomial function.
Determine restrictions on the input variable $x$ .
Polynomial functions are defined for all real numbers. There are no square roots of negative numbers, no denominators that could be zero, and no logarithms of non-positive numbers. Therefore, there are no restrictions on the values $x$ can take.
State the domain.
The domain of the function is all real numbers.
In set-builder notation:
$\boxed{\left\{x \mid x \in \mathbb{R}\right\}}$
In interval notation:
$\boxed{\left(-\infty, \infty\right)}$

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F(x) = 4x² − 1

Answer

Step-by-step solution

Identify the type of function.

Determine restrictions on the input variable xxx.

State the domain.

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Determine restrictions on the input variable $x$ .