SUMMARY
The inverse of the function f(x) = (2x-5)/(7x+4) can be found by rearranging the equation to solve for y. Starting with x = (2y-5)/(7y+4), multiply both sides by (7y+4) to eliminate the fraction. This leads to the equation 7xy + 4x - 2y = -5. By isolating terms with y and factoring, the final form y = (4x + 5)/(2 - 7x) is obtained, providing the inverse function.
PREREQUISITES
- Understanding of algebraic manipulation and rearranging equations
- Familiarity with functions and their inverses
- Knowledge of factoring expressions
- Basic skills in solving linear equations
NEXT STEPS
- Practice finding inverses of other rational functions
- Learn about the graphical representation of functions and their inverses
- Explore the concept of one-to-one functions and their significance in finding inverses
- Study the implications of inverse functions in calculus, particularly in relation to derivatives
USEFUL FOR
Students studying algebra, particularly those learning about functions and their inverses, as well as educators looking for examples of rational function manipulation.