inverse function question

[Guest]

Okay,

the problem is

y= 5e^x+3/ 7-e^x

i need the inverse of this...

i know the e^x can become ln(x) ...

can the 5 go as an exponent?

And i'm not very good with the fraction and inverse...
would i have to distribute y to the multiplied demoniator?

 

[stapel]

I'm not sure what you mean by e^x "becoming" ln(x) -- they are not the same thing -- and I'm not sure how you want to turn the "5" into an exponent, nor on what base....?

You have posted:

. . . . .\(\displaystyle \large{y\mbox{ }= \mbox{ }5e^x \mbox{ } + \mbox{ }\frac{3}{7} \mbox{ }- \mbox{ }e^x}\)

Is that what you meant, or did you mean something more along the lines of the following?

. . . . .\(\displaystyle \large{y\mbox{ } = \mbox{ }\frac{5e^x \mbox{ }+ \mbox{ }3}{7 \mbox{ }- \mbox{ }e^x}}\)

The usual process for finding an inverse is as follows:

. . . . .1) Rename "f(x)" as "y".
. . . . .2) Solve for "x=".
. . . . .3) Switch "x" and "y".

The new "y" is the inverse. If the inverse is a function, then:

. . . . .4) Rename the new "y" as "f^-1(x)".

How far have you gotten in this process? Please reply showing your steps.

Thank you.

Eliz.