Find the inverse function of f.

Question

f(x) = 8x + 6

 

 

f −1(x) = ?

Answer 1

f(x) = 8x + 6

 

Here's the procedure to find the inverse function, f^-1(x).

1. Replace the f(x) with a y: y = 8x + 6
2. Switch the x's and y's: x = 8y + 6
3. Solve for y:

  x = 8y + 6

  x-6 = 8y

  (1/8)x - (3/4) = y = f^-1(x)

     4. Check your answer.  If it's right, then f o f^-1(x) = x  (composition of f and f^-1)

  f o f^-1 = 8*f^-1(x) + 6

             = 8*(x/8 - 3/4) + 6

             = x - 6 + 6

             = x

 Check!