To determine the inverse of the function [tex]\( F(x) = 9x \)[/tex], let’s follow the systematic steps to find the inverse.
1. Set the function equal to [tex]\( y \)[/tex]:
[tex]\[
y = 9x
\][/tex]
2. Solve for [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex]:
To isolate [tex]\( x \)[/tex], we need to divide both sides of the equation by 9:
[tex]\[
x = \frac{y}{9}
\][/tex]
3. Express the inverse function:
Since the inverse function, denoted as [tex]\( F^{-1}(x) \)[/tex], switches the roles of [tex]\( x \)[/tex] and [tex]\( y \)[/tex], we replace [tex]\( y \)[/tex] with [tex]\( x \)[/tex] in the equation:
[tex]\[
F^{-1}(x) = \frac{x}{9}
\][/tex]
Therefore, the inverse of the function [tex]\( F(x) = 9x \)[/tex] is [tex]\( F^{-1}(x) = \frac{x}{9} \)[/tex].
Hence, the correct answer is:
A. [tex]\( F^{-1}(x) = \frac{x}{9} \)[/tex]
