How do you find the inverse of the function f(x) = 4x + 12?

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To find the inverse of the function f(x) = 4x + 12, we follow a series of steps:

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

    y = 4x + 12
  2. Swap x and y: To find the inverse, interchange x and y:

    x = 4y + 12
  3. Solve for y: Now, solve this equation for y. Start by isolating the term with y:
    • Subtract 12 from both sides:
      x - 12 = 4y
    • Now, divide both sides by 4 to solve for y:
      y = \frac{x - 12}{4}
  4. Write the inverse function: Now that we have solved for y, we can express the inverse function:

    f-1(x) = \frac{x - 12}{4}

So, the inverse of the function f(x) = 4x + 12 is:

f-1(x) = \frac{x – 12}{4}

This means that if you input a value into the inverse function, it will yield the original value that was input into the function f(x). For example, if you input f-1(24), you will retrieve back:

f-1(24) = \frac{24 - 12}{4} = \frac{12}{4} = 3

Thus, when 3 is input into the original function f(x), it produces:

f(3) = 4(3) + 12 = 12 + 12 = 24

This confirms the correctness of the inverse calculation.

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