Math Problem Statement
Given that f(x) = x^2 - 5 and g(x) = -2x + 3, find (f/g)(3/2), if it exists.
Solution
The problem asks to find , given the functions:
Step 1: Define the function
The expression means:
Step 2: Substitute into and
-
First, calculate :
-
Next, calculate :
Step 3: Check the result
Since , the function is undefined at . Division by zero occurs, meaning does not exist.
Conclusion:
The expression does not exist because .
Would you like further details or have any questions?
Here are 5 related questions for practice:
- What happens if we try to evaluate for other values of ?
- How do you determine where a function like is undefined?
- Can you find the domain of ?
- What is the behavior of the function as approaches ?
- How can you use limits to analyze functions with undefined points?
Tip: Always check the denominator before substituting values into rational functions to avoid dividing by zero.
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Math Problem Analysis
Mathematical Concepts
Algebra
Rational Functions
Division by Zero
Formulas
f(x) = x^2 - 5
g(x) = -2x + 3
Rational function: (f/g)(x) = f(x)/g(x)
Theorems
Undefined functions when dividing by zero
Suitable Grade Level
Grades 10-12