Find Inverse Function & Domain of f(x)= 1/(1+x)

In summary, the conversation was about finding the inverse of a given function and determining its domain. The function given was f(x)= 1/(1+x) and the inverse function was found to be y= (1/x)- 1. The main concern was finding the domain of the inverse function, with the potential issue being the value of 0. StatusX also mentioned a possible link to consider.
  • #1
jacy
76
0
Hello,
In this problem i have to find the inverse of the given function and the domain on which its valid. Here is the function

f(x)= 1/(1+x)

this is what i have done

y= 1/(1+x)

interchanging x and y
x= 1/(1+y)

y= (1/x)- 1

this is my inverse function.

Now i need to find the domain. Can someone please help me with that, thanks.
 
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  • #2
Do you mean the domain of the inverse function? What do you think could cause a problem for the domain, which x-value(s)?
 
  • #3
Also, what value does the original function never take on? Clearly, there shouldn't be a well defined value of the inverse function at this point.
 
  • #4
TD said:
Do you mean the domain of the inverse function? What do you think could cause a problem for the domain, which x-value(s)?

Yes i need to find the domain of the inverse function.
The value that can cause a problem is 0.
 
  • #5
Is there any other value which could cause a problem?
And do you see the link with what StatusX told you?
 

FAQ: Find Inverse Function & Domain of f(x)= 1/(1+x)

What is an inverse function?

An inverse function is a function that "undoes" the original function. In other words, if the original function takes an input x and produces an output y, the inverse function takes y as its input and produces x as its output.

How do you find the inverse function of a given function?

To find the inverse function, we first replace the function's output (y) with x and the input (x) with y. Then, we solve for y. The resulting equation will be the inverse function of the original function.

What is the domain of the given function f(x)= 1/(1+x)?

The domain of f(x)= 1/(1+x) is all real numbers except for -1, since division by 0 is undefined. In interval notation, the domain can be expressed as (-∞, -1) U (-1, ∞).

How do you determine the domain of a function?

The domain of a function is the set of all possible input values (x) for which the function is defined. To determine the domain, we need to consider any restrictions or limitations on the input values based on the given function.

Can a function have multiple inverse functions?

No, a function can only have one inverse function. This is because an inverse function must pass the vertical line test, meaning that each input (x) must correspond to only one output (y). If a function has multiple outputs for the same input, it would not pass the vertical line test and therefore cannot have an inverse function.

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