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what is the inverse function of f(x)=6x+11

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3 Answers

The easiest way to find the inverse of a function in my opinion is to first change the f(x) back into y and swap your x's and y's. Doing these things gives you:

x = 6y + 11. After you do this simply solve for y and your answer will be the inverse.

start by substracting 11 on both sides of the equation then divide both sides by 6. this should give you y = (x-11)/6

Comments

Agreed Xavier. Except at the very end, you should use f-1(x) = ...   instead of y = ... and of course in slope intercept form you have, f-1(x) = (1/6)x - (11/6)

kim

Correct. I typed the solution right before I began a session with a student so I had to speed things up a little therefore I didn't display the best use of notation.

Comment

Let's rewrite the function notation by using "y" term.

ƒ(x) = 6x + 11
  y = 6x + 11 , let's solve this equation for "x"

6x = y - 11
  x = (1/6) y - 11/6

Now, switch the "x" and "y"

  y = (1/6) x - 11/6

In function notation:

 ƒ - 1(x) = (1/6) x – 11/6  

Inverse fucntions are symmetric with respect to line y=x. Mathematically it can be written as

                                                          f(g) = x

where g(x) is the inverse to f(x) (g = f-1). But

      f(g) = 6g +11   and thus 6g + 11 = x. Hence it follows  g(x) = (x-11)/6