Math Problem Statement
What is the inverse of g(x) = 1/(x - 1) and is it a function?
Solution
To find the inverse of the function and determine whether the inverse is a function, let's follow these steps:
Step 1: Find the inverse of
- Start by writing .
- Swap and to find the inverse:
- Solve for :
So, the inverse function is .
Step 2: Check if the inverse is a function
The inverse, , is indeed a function because each input produces a unique output , except for , which is outside the domain.
Conclusion
The correct choice from the given options is:
Would you like more details or have any questions?
Related Questions:
- How do you determine the domain and range of the inverse function?
- What are the conditions for a function to have an inverse?
- How can you verify if an inverse function is a function using the horizontal line test?
- What are the asymptotes of the function and its inverse?
- How do you graph both a function and its inverse on the same coordinate plane?
Tip: To find the inverse of a function, swap and and solve for the new .
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Math Problem Analysis
Mathematical Concepts
Inverse Functions
Algebra
Formulas
y = 1/(x - 1)
x = 1/(y - 1)
y = (x + 1)/x = 1 + 1/x
Theorems
The inverse of a function
Solving for the inverse of a function
Horizontal Line Test for determining if the inverse is a function
Suitable Grade Level
Grades 10-12