Math Problem Statement
Let f(x)= x-5 and g(x)= x^2-1 be defined as in the previous example. Express the following functions as the sum, difference, quotient, or product of f and g of r(x)=x-5\2x^2-2
Solution
To express the function as a combination of and , we start by analyzing how can be rewritten in terms of and .
Step 1: Factor the denominator of
First, we factor the denominator : Thus, we can rewrite as:
Step 2: Express in terms of and
Since , we can substitute into the expression:
Final Answer:
The function can be expressed as: This represents the quotient of and .
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- How do you express the sum of and ( g(x
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Math Problem Analysis
Mathematical Concepts
Functions
Quotient of Functions
Factorization
Formulas
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Theorems
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Suitable Grade Level
High School
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