Math Problem Statement

inverse function of f(x) = x/2 +2

Solution

To find the inverse of the function f(x)=x2+2f(x) = \frac{x}{2} + 2, follow these steps:

  1. Replace f(x)f(x) with yy: y=x2+2y = \frac{x}{2} + 2

  2. Swap xx and yy: x=y2+2x = \frac{y}{2} + 2

  3. Solve for yy: x2=y2x - 2 = \frac{y}{2} y=2(x2)y = 2(x - 2) y=2x4y = 2x - 4

  4. Replace yy with f1(x)f^{-1}(x): f1(x)=2x4f^{-1}(x) = 2x - 4

So, the inverse function of f(x)=x2+2f(x) = \frac{x}{2} + 2 is f1(x)=2x4f^{-1}(x) = 2x - 4.

Would you like more details or have any questions?

Here are 5 related questions to explore further:

  1. What is the inverse function of f(x)=x3+5f(x) = \frac{x}{3} + 5?
  2. How do you verify that two functions are inverses of each other?
  3. What is the inverse of a quadratic function, such as f(x)=x2+3f(x) = x^2 + 3?
  4. How does the graph of a function compare to the graph of its inverse?
  5. What are the conditions for a function to have an inverse?

Tip: Always remember that the inverse of a function, when composed with the original function, should return the input value (i.e., f(f1(x))=xf(f^{-1}(x)) = x and f1(f(x))=xf^{-1}(f(x)) = x).

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Functions
Inverse Functions
Equations

Formulas

-

Theorems

-

Suitable Grade Level

Grades 10-12