Formula of an inverse function

In summary, the conversation discusses finding the formula for the inverse function of f(x)=300/(3+15e^.05x). The attempted solution involves using the cross product trick and rearranging terms to isolate x. The suggestion is made to use the properties of logarithms to simplify the equation.
  • #1
wertlewoo2
2
0

Homework Statement


Find the formula of the inverse function of f(x)=300/(3+15e^.05x).


Homework Equations



f(x)=300/(3+15e^.05x)

The Attempt at a Solution



I'm definitely way off but I got .05y(5x)+ln100=lnx. What I did was multiple the denominator by the y(cross mltiplication) and then tried to factor out e.
 
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  • #2
Welcome to PF!

So you start with y = 300 / (3 + 15 e^(x/20)

and do the cross product trick to get y * (3 + 15e^(x/20)) = 300

and then to:

3 + 15e^(x/20) = 300 / y

Does this help?

You should now move terms and factors to the y side and you should then be able to isolate everything
so that you get x = ...
 
  • #3
@Jedishrfu Thanks so much that was really helpful! Last question do you know how you could be able to take the ln of e to simplify the equation?
 
  • #4
wertlewoo2 said:
@Jedishrfu Thanks so much that was really helpful! Last question do you know how you could be able to take the ln of e to simplify the equation?
I'm sure he does. The real question is do you know how? If you do, take a stab at it.

If you don't, review the properties of logarithms.
 
  • #5
Mark44 said:
I'm sure he does. The real question is do you know how? If you do, take a stab at it.

If you don't, review the properties of logarithms.

:smile:
 

Related to Formula of an inverse function

What is the formula for an inverse function?

The formula for an inverse function is f^-1(x) = y, where y is the original input of the function and x is the output.

How do you find the inverse of a function?

To find the inverse of a function, switch the positions of x and y in the original function and solve for y. This will give you the formula for the inverse function.

What is the relationship between a function and its inverse?

The inverse of a function is essentially the "opposite" of the original function. If the original function takes an input and produces an output, the inverse function takes the output and produces the original input.

What is the importance of inverse functions in mathematics?

Inverse functions are important in mathematics because they allow us to undo a function's operation and retrieve the original input. They are also used to solve equations involving exponential, logarithmic, and trigonometric functions.

What are some properties of inverse functions?

Some properties of inverse functions include: the domain and range of the inverse function are switched, the composition of a function and its inverse results in the input value, and a function has an inverse if and only if it is one-to-one (each input has a unique output).

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