Math Problem Statement
Let f ( x )
1 x + 7
f − 1 ( x )
Solution
To find the inverse function of the given function , we need to follow these steps:
Step 1: Replace with
Let .
Step 2: Solve for
We want to express in terms of . First, subtract 7 from both sides:
Next, take the reciprocal of both sides:
Step 3: Replace with
Now, replace with to get the inverse function:
Thus, the inverse function is:
Would you like more details on the process, or do you have any questions?
Here are 5 related questions to explore:
- What are the domain and range of the original function ?
- How can we verify that for this function?
- What are the domain and range of the inverse function ?
- How does shifting a function vertically (like adding 7) affect its inverse?
- What happens to the graph of compared to ?
Tip: When finding the inverse of a function, always check that the resulting inverse undoes the operations of the original function.
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Math Problem Analysis
Mathematical Concepts
Inverse Functions
Rational Functions
Formulas
Inverse function formula f^{-1}(x)
f(x) = 1/x + 7
f^{-1}(x) = 1/(x - 7)
Theorems
The Inverse Function Theorem
Suitable Grade Level
Grades 10-12