A function is defined by \(h : x \to 2 - \frac{1}{2x - 3}, x \neq \frac{3}{2}\). Find \(h^-1\), the inverse of h.
Question 1 Report
A function is defined by \(h : x \to 2 - \frac{1}{2x - 3}, x \neq \frac{3}{2}\). Find \(h^-1\), the inverse of h.
Answer Details
To find the inverse of a function, you need to switch the roles of x and y, then solve for y. The resulting expression will be the inverse function, denoted as \(h^{-1}\).
Starting with the original function:
\(h : x \to 2 - \frac{1}{2x - 3}, x \neq \frac{3}{2}\)
Switching the roles of x and y:
\(x = 2 - \frac{1}{2y - 3}\)
Solving for y:
\(x - 2 = - \frac{1}{2y - 3}\)
\(-2y + 3 = -\frac{1}{x - 2}\)
\(-2y = -\frac{1}{x - 2} - 3\)
\(y = \frac{1}{2} \cdot \frac{1}{2 - x} + \frac{3}{2}\)
\(y = \frac{3x - 7}{2x - 4}, x \neq 2\)
Therefore, the inverse function is \(h^{-1} : x \to \frac{3x - 7}{2x - 4}, x \neq 2\).
The correct option is (B).
Download The App On Google Playstore
Everything you need to excel in your exams
Personalized AI Learning Chat Assistant
200,000+ Exam Questions Across IGCSE, JAMB, WAEC & NECO
Over 3,900 Lesson Notes
Offline Support - Learn Anytime, Anywhere
Green Bridge Timetable
Literature Summaries & Potential Questions
Track Your Performance & Progress
In-depth Explanations for Comprehensive Learning