What is the inverse of the function f(x) = 2x + 10?

by

To find the inverse of the function f(x) = 2x + 10, we need to follow a few methodical steps.

  1. Replace f(x) with y: Start by rewriting the function as:

    y = 2x + 10

  2. Swap x and y: This step is essential for finding the inverse. We replace y with x and x with y:

    x = 2y + 10

  3. Solve for y: Now, we need to isolate y. Start by subtracting 10 from both sides:

    x – 10 = 2y

    Then, divide both sides by 2:

    y = (x – 10) / 2

  4. Write the inverse function: The inverse function can now be expressed as:

    f-1(x) = (x – 10) / 2

So, the inverse of the function f(x) = 2x + 10 is f-1(x) = (x – 10) / 2.

This process showcases how we systematically find the inverse function by manipulating the original equation. Understanding this concept can be very helpful in different areas of mathematics, including calculus and algebra.

Leave a Comment