Math Problem Statement
Solution
Let's go through each function step by step to find their inverses.
-
:
- To find the inverse, first replace with :
- Switch and :
- Solve for :
- So, the inverse is .
- To find the inverse, first replace with :
-
:
- Replace with :
- Switch and :
- Solve for :
- So, the inverse is .
- Replace with :
-
:
- Replace with :
- Switch and :
- Solve for by cross-multiplying:
- Group the terms with :
- Solve for :
- So, the inverse is .
- Replace with :
-
:
- Replace with :
- Switch and :
- Solve for by cross-multiplying:
- Group the terms with :
- Solve for :
- So, the inverse is .
- Replace with :
-
:
- Replace with :
- Switch and :
- Solve for by cross-multiplying:
- Group the terms with :
- Solve for :
- So, the inverse is .
- Replace with :
Would you like more details on any step? Here are some related questions:
- What is the general process for finding the inverse of a function?
- How can we verify that two functions are inverses of each other?
- Why is switching and a key step in finding the inverse?
- What kind of functions do not have inverses, and why?
- How do we deal with more complex functions, such as those involving higher-degree polynomials, when finding inverses?
Tip: Always check if a function is one-to-one before finding its inverse, as non-invertible functions cannot have proper inverses.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Inverse Functions
Algebra
Formulas
To find the inverse, switch x and y, then solve for y.
Theorems
Inverse Function Theorem: For a function to have an inverse, it must be one-to-one and onto (bijective).
Suitable Grade Level
Grades 10-12
Related Recommendation
How to Find Inverse Functions for Rational, Linear, and Square Root Equations
Inverse Functions: Solving for f^-1(x) in Various Algebraic Functions
Matching Functions with Their Inverses - Rational Function Problem
Solving Inverse Functions and Linear Equations with Application
Solve Inverse Functions for a(x), b(x), and c(x)