inverse functions

[kristoball]

hello, i'm just looking for some help with inverse functions when it comes to ln operations. For example, Find the inverse function of y = 2+5ln(8x+10).
I know i need to solve for x, but i don't know where to start. If anyone knows how to begin a problem such as this, please help me out. Thanks!

I also have another problem on my homework involving inverse equations. I'm asked to find the inverse of f(x) = (6x+7)/(9x+11). My final answer was y=(7-11y)/(9y-6). This was not one of the available answers. Does anyone else come up with anything different? If so, please show me your work, or point out where I messed up. My work leading to my answer is below.

f(x) = (6x+7)/(9x+11)
y = (6x+7)/(9x+11)
y(9x+11)=6x+7
9xy+11y=6x+7
9xy-6x=7-11y
x(9y-6)=7-11y
x=(7-11y)/(9y-6)
y=(7-11y)/(9y-6)

 

[Mrspi]

hello, i'm just looking for some help with inverse functions when it comes to ln operations. For example, Find the inverse function of y = 2+5ln(8x+10).
I know i need to solve for x, but i don't know where to start. If anyone knows how to begin a problem such as this, please help me out. Thanks!

I also have another problem on my homework involving inverse equations. I'm asked to find the inverse of f(x) = (6x+7)/(9x+11). My final answer was y=(7-11y)/(9y-6). This was not one of the available answers. Does anyone else come up with anything different? If so, please show me your work, or point out where I messed up. My work leading to my answer is below.

f(x) = (6x+7)/(9x+11)
y = (6x+7)/(9x+11)
At this point, I would SWITCH the xs and the ys:

x = (6y + 7)/(9y + 11)
and then SOLVE for y.....
y(9x+11)=6x+7
9xy+11y=6x+7
9xy-6x=7-11y
x(9y-6)=7-11y
x=(7-11y)/(9y-6)
y=(7-11y)/(9y-6)

Continuing from what I said in red above:

x = (6y + 7)/(9y + 11)

x(9y + 11) = 6y + 7

9xy + 11x = 6y + 7

We want to solve for y....so get all terms containing y on one side, and everything else on the other side:

9xy - 6y = 7 - 11x

Factor "y" out of both terms on the left side:

y(9x - 6) = 7 - 11x

Divide both sides of the equation by (9x - 6):

y = (7 - 11x) / (9x - 6)

Somehow, you got your xs and ys confused. This is just a matter of being CAREFUL, I think.