Math Problem Statement
Solution
To solve this problem, let’s analyze the pairs of functions and , compute the compositions and , and determine whether they are inverses by verifying if both compositions equal .
Problem (a):
Step 1: Compute
Substitute into : Simplify:
Step 2: Compute
Substitute into : Simplify:
Conclusion for (a):
Since and , and are inverses of each other.
Problem (b):
Step 1: Compute
Substitute into : Simplify:
Step 2: Compute
Substitute into : Simplify:
Conclusion for (b):
Since and , and are inverses of each other.
Final Answers:
- (a): and are inverses of each other.
- (b): and are inverses of each other.
Would you like further clarification on any step? Let me know!
Related Questions:
- What does it mean for two functions to be inverses of each other?
- How do you find the inverse of a function algebraically?
- Can you provide an example of two functions that are not inverses?
- What happens if but ?
- How does domain and range impact whether functions can be inverses?
Tip:
When verifying inverses, always calculate both and to confirm they equal .
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Function Composition
Inverse Functions
Simplifying Algebraic Expressions
Formulas
f(g(x))
g(f(x))
Theorems
Definition of Inverse Functions: f(g(x)) = x and g(f(x)) = x
Suitable Grade Level
Grades 10-12
Related Recommendation
Verify Inverse Functions Algebraically: f(x) = (x - 2)/7 and g(x) = 7x + 2
Verify Inverse Functions: Composition of f(x) = -2x + 3 and g(x) = -1/2(x - 3)
Inverse Functions: Verifying if f(x) = 2x - 3 and g(x) = (x + 2) / 3 are Inverses
Solving Function Composition and Inverse Functions
How to Determine if Two Functions Are Inverse: f(x) = 2x + 5 and g(x) = (x - 5)/2