What is the inverse of the function f(x) = 4x + 8?

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To find the inverse of the function f(x) = 4x + 8, we need to follow a series of systematic steps. The goal is to express the input variable (x) in terms of the output variable (y).

  1. Step 1: Start by replacing f(x) with y:
    y = 4x + 8
  2. Step 2: Next, we need to solve this equation for x. To do this, we first isolate the term containing x:
  3. y - 8 = 4x
  4. Step 3: Now, divide both sides by 4 to solve for x:
    x = \frac{(y - 8)}{4}
  5. Step 4: This expression represents the input value x in terms of y. To write the inverse function, we swap x and y:
    f^{-1}(x) = \frac{(x - 8)}{4}

Thus, the inverse of the function f(x) = 4x + 8 is:

f-1(x) = \frac{(x – 8)}{4}

This result tells us that if you take any output value from the original function and apply the inverse function, you will retrieve the corresponding input value.

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