Math Problem Statement
Solution
Let's go through the problem you posted.
We are given two functions:
(a) Find .
This means we need to evaluate at .
-
First, find :
-
Now, find :
-
Now, calculate :
(b) Find all values that are NOT in the domain of .
The domain of consists of all values of for which . So, we need to find when .
equals zero when or . Thus, the values that are not in the domain of are and .
Final Answers:
- (a)
- (b) Values not in the domain of :
Would you like further clarification or details on any part of this? Here are some related questions you might find useful:
- How do you determine the domain of a quotient of functions?
- What happens if you try to divide by zero in functions?
- How do you factor quadratics like ?
- What are the key differences between the domain of and ?
- How can you visually represent the domain and range of a function?
Tip: Always remember to check for values that make the denominator zero when dealing with rational functions!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Functions
Domain and Range
Quotient of Functions
Formulas
f(x) = x - 5
g(x) = (x - 4)(x + 4)
(f/g)(x) = f(x) / g(x)
Theorems
Division by Zero Theorem (the denominator cannot be zero)
Zero Product Property (a product of two numbers is zero if at least one of the numbers is zero)
Suitable Grade Level
Grades 9-11
Related Recommendation
Simplifying the Quotient of Functions f(x) = 4x + 20 and g(x) = x^2 - 3x - 40
(f/g)(x): Find (f/g)(x) for f(x)=8x−56 and g(x)=x^2+2x−63
Evaluating Rational Functions: f(x) = x^2 + 1, g(x) = x - 4
Quotient of Functions: Solve (f/g)(x) = (x + 3) / (2x - 5)
Difference Quotient for Rational Function f(x) = (x - 4) / (x - 5)