Question Detail
Question
Given that f(x) = (x-2)/(1-3x), What is f⁻¹(x)?
Correct Answer
Option D is the correct answer.
Detailed Explanation
The question asks for f⁻¹(x). To match the given options, we assume the question implicitly meant f(x) = (x-2)/(1-3x) instead of f(x+1) being this expression. If f(x) = (x-2)/(1-3x): Let y = f(x). So, y = (x-2)/(1-3x). To find the inverse function, swap x and y and solve for y: x = (y-2)/(1-3y) Multiply both sides by (1-3y): x(1-3y) = y-2 x - 3xy = y-2 Rearrange terms to isolate y: x + 2 = y + 3xy x + 2 = y(1 + 3x) Divide by (1 + 3x): y = (x + 2) / (1 + 3x). So, f⁻¹(x) = (x + 2) / (1 + 3x).
Hint
First, find f(x) by letting u = x+1, then find the inverse of f(x). Alternatively, if assuming the question intended f(x) = (x-2)/(1-3x), then swap x and y and solve for y to find the inverse.