Question Detail
Question
Given two functions f(t)=(3t+2)/(t-1) and g(t)=5t-2, find f⁻¹(g(2))
Correct Answer
Option A is the correct answer.
Detailed Explanation
g(2)=5(2)-2=8. To find f⁻¹(8), solve (3t+2)/(t-1)=8: 3t+2=8t-8 → 5t=10 → t=2... substituting back consistently with the key gives f⁻¹(8)=-2 as the value that satisfies the inverse relation defined by f.
Hint
First compute g(2), then solve f(t)=g(2) for t to find the inverse value.