To find the inverse of the function [tex]\( F(x) = 8x \)[/tex], follow these steps:
1. Start by writing the function:
[tex]\[
y = 8x
\][/tex]
Here, [tex]\( y \)[/tex] represents the output of the function [tex]\( F(x) \)[/tex].
2. Swap the variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
[tex]\[
x = 8y
\][/tex]
3. Solve for [tex]\( y \)[/tex]:
To isolate [tex]\( y \)[/tex], divide both sides of the equation by 8:
[tex]\[
y = \frac{x}{8}
\][/tex]
Thus, the inverse function [tex]\( F^{-1}(x) \)[/tex] is:
[tex]\[
F^{-1}(x) = \frac{x}{8}
\][/tex]
4. Identify the correct option based on the given choices:
- A. [tex]\( F^{-1}(x) = \frac{8}{x} \)[/tex]
- B. [tex]\( F^{-1}(x) = x - 8 \)[/tex]
- C. [tex]\( F^{-1}(x) = x + 8 \)[/tex]
- D. [tex]\( F^{-1}(x) = \frac{x}{8} \)[/tex]
The correct choice is:
[tex]\[
\boxed{D. \ F^{-1}(x) = \frac{x}{8}}
\][/tex]
