Math Problem Statement
Find the inverse of f(x) = (-4x - 5) / (4x - 3).
Solution
To find the inverse of the given function , follow these steps:
Steps to find the inverse:
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Replace with :
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Swap and :
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Solve for : Multiply both sides by to eliminate the denominator:
Distribute :
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Group all terms involving on one side:
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Factor out :
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Solve for :
Thus, the inverse function is:
Let me know if you'd like more details on any step, and feel free to ask questions!
Related Questions:
- How do you verify if two functions are inverses of each other?
- Can every function have an inverse? What are the conditions?
- How does the behavior of a function change when you consider its inverse?
- What does it mean graphically when a function and its inverse are plotted?
- What role do one-to-one functions play in finding inverses?
Tip:
When solving for the inverse, always ensure the function is one-to-one (passes the horizontal line test) to confirm that an inverse exists.
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Math Problem Analysis
Mathematical Concepts
Functions
Inverse Functions
Formulas
Inverse Function Calculation: y = f(x), x = f(y)
Theorems
Function Inversion
Suitable Grade Level
College