How do you find the inverse function of f(x) = 5x + 4 and evaluate it at x = 19?

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Finding the Inverse Function

To find the inverse function of f(x) = 5x + 4, we need to follow these steps:

  1. Start by replacing f(x) with y:

    y = 5x + 4
  2. Next, swap x and y:

    x = 5y + 4
  3. Now, solve for y:
    • Subtract 4 from both sides: x – 4 = 5y
    • Divide by 5: y = (x – 4) / 5

Thus, the inverse function is:

f-1(x) = (x – 4) / 5

Evaluating the Inverse Function at x = 19

Now, let’s evaluate the inverse function at x = 19:

  • Substitute 19 into the inverse function:

    f-1(19) = (19 – 4) / 5
  • Calculate the result:
    f-1(19) = 15 / 5 = 3

Therefore, the value of the inverse function when x = 19 is 3.

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