Math Problem Statement
Consider the function f(x)=(ax+3)/(x-b) Find a and b given that y = f(x) with equations x=-1 and y=2
Solution
To solve for and in the function , we use the information provided: when , .
Step 1: Substitute and into the function
The function becomes:
Simplify:
Multiply through by the denominator (assuming ):
Simplify:
Rearrange to express in terms of :
Step 2: Determine additional conditions
The problem does not give enough information for a unique solution. To find both and , additional conditions (e.g., another point on the curve) are needed.
Would you like to provide more details or constraints? Alternatively, I can outline typical approaches to deduce values in similar problems. Let me know!
Related Questions:
- How can the vertical asymptote help determine ?
- What happens to and if must be continuous at ?
- How would the solution change if another pair is provided?
- How can this function's symmetry be analyzed to simplify solving for and ?
- Can derivatives of provide information about and ?
Tip: Always check for the domain restrictions of a rational function; the denominator must not equal zero.
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Math Problem Analysis
Mathematical Concepts
Algebra
Rational Functions
Equations
Formulas
f(x) = (ax + c) / (x - b)
Theorems
Solving equations by substitution
Domain restrictions of rational functions
Suitable Grade Level
Grades 9-11
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