Hey can you give me a step by step solution on how to calculate the inverse function in fractional form , and please include the formula on how to check that one.

To find the inverse of a function, particularly when dealing with fractional forms, you can follow these steps. Let's assume you have a function \( f(x) \) and you want to find \( f^{-1}(x) \), its inverse. Below are the step-by-step instructions:

### Step-by-Step Process to Find the Inverse:

#### 1. **Start with the function:**
   Let's assume the function is given as:
   \[
   f(x) = \frac{ax + b}{cx + d}
   \]
   where \( a, b, c, d \) are constants.

#### 2. **Replace \( f(x) \) with \( y \):**
   Rewrite the function using \( y \) instead of \( f(x) \):
   \[
   y = \frac{ax + b}{cx + d}
   \]

#### 3. **Swap \( x \) and \( y \):**
   To find the inverse, we swap \( x \) and \( y \). This gives:
   \[
   x = \frac{ay + b}{cy + d}
   \]

#### 4. **Solve for \( y \):**
   Now solve this equation for \( y \):
   \[
   x(cy + d) = ay + b
   \]
   Expand both sides:
   \[
   xcy + xd = ay + b
   \]
   Collect all terms involving \( y \) on one side:
   \[
   xcy - ay = b - xd
   \]
   Factor out \( y \) on the left-hand side:
   \[
   y(xc - a) = b - xd
   \]


Hey can you give me a step by step solution on how to calculate the inverse function in fractional form, and please include the formula on how to check that one.

Learn how to calculate the inverse of a fractional function with step-by-step instructions. This problem involves functions, algebraic fractions, and key formulas for checking the inverse. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation