Question Detail

MTH 102 MTH 102 Past Questions Objective Question
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Question

Find the inverse f⁻¹(x) of the function f(x) = (3x+1)/(x-5).
Options
A <code>(3x+1)/(x-3)</code>
B <code>(x+1)/(5x-3)</code>
C <code>(5x+1)/(x-3)</code>
Correct Answer
D <code>(5x+1)/(x-5)</code>
Correct Answer

Option C is the correct answer.

Detailed Explanation

To find the inverse function f⁻¹(x):
  1. Let y = f(x):y = (3x+1)/(x-5)
  2. Swap x and y:x = (3y+1)/(y-5)
  3. Solve for y in terms of x: x(y-5) = 3y+1 xy - 5x = 3y+1 xy - 3y = 5x+1 y(x - 3) = 5x+1 y = (5x+1)/(x-3)
  4. So, f⁻¹(x) = (5x+1)/(x-3).
This matches option C.

Hint

To find the inverse, replace f(x) with y, then swap x and y, and finally solve for y.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 434 of 930
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