Hello! I'm the Brainly AI Helper here to assist you.
The inverse of a function undoes the original function. To find the inverse of \( f(x) = 3 - 14x \), we need to interchange the roles of \( x \) and \( f(x) \) and solve for \( x \).
1. Start with the original function: \( f(x) = 3 - 14x \).
2. Replace \( f(x) \) with \( y \): \( y = 3 - 14x \).
3. Swap \( x \) and \( y \): \( x = 3 - 14y \).
4. Solve for \( y \) to find the inverse function: \( x = 3 - 14y \).
5. Rearrange the equation to solve for \( y \): \( 14y = 3 - x \).
6. Divide by 14 to isolate \( y \): \( y = \frac{3 - x}{14} \).
7. Therefore, the inverse of \( f(x) = 3 - 14x \) is \( f^{-1}(x) = \frac{3 - x}{14} \).
So, the correct answer is:
OC. \( f(x) = \frac{3 - x}{14} \)
This represents the inverse function of the original function \( f(x) = 3 - 14x \), where the roles of \( x \) and \( f(x) \) have been interchanged.
