Math Problem Statement
If f(x) = 11 6x + 5 and g(x) =
2x + 7 , compute the compositions (f ∘ g)(1) and (g ∘ f)(1).
Solution
Let's compute the compositions and step by step, using the given functions:
1. Compute
The composition means we first apply , then apply to the result.
- Find :
- Now apply to : Thus, .
2. Compute
The composition means we first apply , then apply to the result.
- Find :
- Now apply to : Thus, .
Final Answer:
Would you like more details on any of the steps?
Here are 5 related questions:
- What is the general formula for ?
- How does the composition of functions differ from addition or multiplication of functions?
- Can we reverse the composition order for any two functions?
- What happens if we change the given functions and ?
- What would and look like as general expressions?
Tip: Always be cautious about the order of compositions; is not the same as .
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Function Composition
Algebra
Formulas
(f ∘ g)(x) = f(g(x))
(g ∘ f)(x) = g(f(x))
Theorems
Composition of Functions
Suitable Grade Level
Grades 10-12