Math Problem Statement

For the function f(x) = 9x + 4, find f^{-1}(x).

Solution

We are given the function f(x)=9x+4f(x) = 9x + 4, and the task is to find the inverse of this function, denoted by f1(x)f^{-1}(x).

Steps to find the inverse function:

  1. Start with the original function: y=9x+4y = 9x + 4 where y=f(x)y = f(x).

  2. Swap xx and yy to prepare for solving for the inverse: x=9y+4x = 9y + 4

  3. Solve for yy (which will be the inverse function): x4=9yx - 4 = 9y y=x49y = \frac{x - 4}{9}

So, the inverse function is: f1(x)=x49f^{-1}(x) = \frac{x - 4}{9}

Answer:

The correct option is: f1(x)=x49f^{-1}(x) = \frac{x - 4}{9}

Do you have any further questions or would you like a more detailed explanation?

Related Questions:

  1. How do you determine if a function has an inverse?
  2. Can a function have more than one inverse?
  3. What are the steps to verify that two functions are inverses?
  4. What is the domain and range of the inverse function?
  5. How would you graph both the function and its inverse?

Tip: Always check that a function is one-to-one (passes the horizontal line test) before finding its inverse!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Inverse Functions

Formulas

f(x) = 9x + 4
f^{-1}(x) = (x - 4)/9

Theorems

Inverse Function Theorem

Suitable Grade Level

Grades 9-12