Math Problem Statement
Solution
The problem involves finding the domains of the given functions. Let's go through each part of the problem.
Functions Given
(a) Domain of
For , the function is undefined where the denominator is zero. Therefore: The domain of is all real numbers except and . In interval notation:
(b) Domain of
For , this is a linear function, which is defined for all real numbers. So:
(c) Domain of (Composition of and )
To find the domain of , we need to evaluate . The function .
We need to find when the denominator is zero: This results in or .
So, the domain of is all real numbers except and . In interval notation:
Summary of Answers
- (a) Domain of :
- (b) Domain of :
- (c) Domain of :
Would you like further details or have any questions?
Here are 5 related questions that expand on the above:
- What is the range of ?
- How would the domain change if ?
- Can you find the domain of instead of ?
- How does adding a constant to the numerator of affect its domain?
- If were a trigonometric function, how would you approach finding the domain of ?
Tip: Always start by finding points where the denominator is zero when working with rational functions to determine the domain.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Rational Functions
Composition of Functions
Formulas
f(x) = x / (x^2 - 1)
g(x) = x + 1
f(g(x)) = (x + 1) / ((x + 1)^2 - 1)
Theorems
To find the domain of a rational function, exclude values that make the denominator zero.
For composition of functions, exclude values that make the inner or outer function undefined.
Suitable Grade Level
Grades 10-12
Related Recommendation
Composition of Rational Functions: f(x) = (1 + x)/(1 - x) and g(x) = x/(1 - x)
Finding the Domain of a Composed Function f(g(x)) with Rational Functions
Finding Compositions and Domains for f(x) = (1 - x) / 22x and g(x) = 1 / (1 + 22x)
Find (f + g)(x), (f - g)(x), (fg)(x), and (f/g)(x) for f(x) = √(5x - 1) and g(x) = 1/x
Determine the Domain of Composite Functions for f(x) = 1/x and g(x) = 1/(5x)