Math Problem Statement

Answer

If f(x) = 2 / (x - 3), find f(5).

Solution

The given function is:

f(x)=2x3f(x) = \frac{2}{x - 3}

We are asked to find f(5)f(5), which means substituting x=5x = 5 into the function.

f(5)=253=22=1f(5) = \frac{2}{5 - 3} = \frac{2}{2} = 1

Thus, f(5)=1f(5) = 1.

Would you like further clarification or have any questions?

Here are five related questions:

  1. What happens to f(x)f(x) as xx approaches 3?
  2. Can you find f(0)f(0) for the same function?
  3. How would the function change if it was f(x)=3x4f(x) = \frac{3}{x - 4}?
  4. What is the domain of the function f(x)=2x3f(x) = \frac{2}{x - 3}?
  5. How does f(x)f(x) behave as xx approaches infinity?

Tip: When evaluating functions, always ensure that the denominator does not result in zero to avoid undefined expressions.

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Substitution

Formulas

f(x) = 2 / (x - 3)

Theorems

Function evaluation by substitution

Suitable Grade Level

Grades 9-10