Math Problem Statement
if f(x) = e^(4x-3), find f^-1(x)
Solution
To find the inverse function for the given function , follow these steps:
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Start with the function:
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Swap and to solve for the inverse function:
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Take the natural logarithm (ln) of both sides to solve for :
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Isolate :
So, the inverse function is:
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Related Questions:
- What is the domain of ?
- How do you determine if is one-to-one?
- What is the range of the original function ?
- How do you differentiate ?
- Can this method be used for functions with different exponents, such as ?
Tip: Always remember that the domain of the inverse function is the range of the original function, and vice versa.
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Math Problem Analysis
Mathematical Concepts
Exponential Functions
Inverse Functions
Natural Logarithm
Formulas
Inverse function formula for exponential functions
Theorems
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Suitable Grade Level
Advanced High School and above