What is the inverse function of f(x) = 2x + 6?

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To find the inverse function of f(x) = 2x + 6, we need to follow a few logical steps. The first step is to replace f(x) with y:

Step 1: Rewrite the function:

y = 2x + 6

Step 2: Swap x and y:

x = 2y + 6

Step 3: Solve for y. To do this, isolate y:

  • Subtract 6 from both sides:
  • x – 6 = 2y

Step 4: Divide both sides by 2:

y = (x – 6) / 2

Step 5: Finally, we write the inverse function:

f-1(x) = (x – 6) / 2

Thus, the inverse function of f(x) = 2x + 6 is f-1(x) = (x – 6) / 2. This means that if you input a value into the inverse function, you’ll get out the corresponding value that was originally input into the function. In simpler terms, the inverse function ‘undoes’ the effect of the original function.

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