Answer :
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]
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]
