HELP! PRE-CALC QUESTION? LOGARITHMIC FUNCTIONS!?

[ohyes_itsbekah]

Write the inverse of f(x) = 6x+1

f^-1(x) = ???

PLEASE HELP!
I know how to do normal inverse functions...these are logarithmic functions. The answer should look something like f^-1(x) = log(sub 6)x+1...but I never learned what to do with the x+1...

 

[James H]

y = 6x + 1

x = 6y + 1 (replace x's with y's)

x - 1 = 6y

(x-1)/6 = y (get y on its own)

f^-1(x) = (x - 1)/6

 

[friendlyhelp04]

Inverses are easy!

Just swap the x & y variables, then re-solve for y. Keep in mind that y and f(x) mean the same thing, so you can rewrite your equation as:

f(x) = 6x + 1
y = 6x +1

Now swap x & y (where there's an x, put a y, and where there's a y, put an x...yes, it really is as easy as it sounds).

x = 6y + 1

Solve for y:

x - 1 = 6y

y = (1/6)(x - 1)

So your inverse is: f^-1(x) = (1/6)(x-1)

 

[samitang]

y=6x+1

the inverse is

x=6y+1