Math Problem Statement
Assume that the function
f
is a one-to-one function.
(a) If
f
(
8
)
7
, find
f
−
1
(
7
)
.
Your answer is
Solution
Since is a one-to-one function, the inverse function undoes the action of . That is, if , then the inverse .
Thus, the answer is:
Would you like a detailed explanation on inverse functions, or do you have any other questions?
Here are 5 related questions you might find helpful:
- What does it mean for a function to be one-to-one?
- How do you verify if a function has an inverse?
- What is the graphical interpretation of inverse functions?
- Can a function have more than one inverse?
- How do you find the inverse of a quadratic function?
Tip: A function is one-to-one if and only if every horizontal line intersects its graph at most once (this is called the Horizontal Line Test).
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Math Problem Analysis
Mathematical Concepts
Inverse Functions
One-to-One Functions
Formulas
f(f−1(x)) = x
f−1(f(x)) = x
Theorems
One-to-One Function Theorem
Inverse Function Property
Suitable Grade Level
Grades 10-12