To determine the [tex]\( x \)[/tex]-intercepts of the function [tex]\( f(x) = x^2 - 81 \)[/tex], we need to find the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 0 \)[/tex].
To do so, let's solve the equation [tex]\( x^2 - 81 = 0 \)[/tex] step-by-step.
1. Start with the given function:
[tex]\[
x^2 - 81 = 0
\][/tex]
2. Add 81 to both sides of the equation:
[tex]\[
x^2 = 81
\][/tex]
3. Take the square root of both sides to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \pm \sqrt{81}
\][/tex]
4. Calculate the square root of 81:
[tex]\[
\sqrt{81} = 9
\][/tex]
5. Include both the positive and negative solutions:
[tex]\[
x = 9 \quad \text{and} \quad x = -9
\][/tex]
Thus, the [tex]\( x \)[/tex]-intercepts of the function [tex]\( f(x) = x^2 - 81 \)[/tex] are [tex]\( x = 9 \)[/tex] and [tex]\( x = -9 \)[/tex].
Given the choices:
A. -9
B. -81
C. -72
D. -36
The correct answer is A. -9.
