Finding the domain of the inverse function

In summary, a domain is the set of all possible input values for a function. To find the domain of an inverse function, you can use the range of the original function as the domain for the inverse function. The domain of an inverse function can be different from the domain of the original function, and if the original function has a restricted domain, the domain of the inverse function will also be restricted. The domain of an inverse function can also be visually determined by graphing it with the original function on the same coordinate plane.
  • #1
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Homework Statement



Let f(x)=e^(-x)-x ,, x belongs to R

Find the domain of f inverse


Homework Equations



Domain of f inverse = range of f


The Attempt at a Solution



we have :

-inf < x < inf
-inf < -x < inf ... (1)
0 < e^(-x) < inf ... (2)

By adding (1) and (2) :

-inf < e^(-x) - x < inf

So domain of f = R = range of f inverse.

Is this correct?

Can I add the inequalities together?
 
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  • #2
Ignore my last post. I read the function wrong. Yep, the domain of the inverse is all real numbers.
 
  • #3
Thanks.
 

Related to Finding the domain of the inverse function

1. What is a domain?

A domain is the set of all possible input values for a function.

2. How do you find the domain of an inverse function?

To find the domain of an inverse function, you first need to find the range of the original function. Then, you can use the range as the domain for the inverse function, as the input values for the inverse function will be the output values of the original function.

3. Can the domain of an inverse function be different from the domain of the original function?

Yes, the domain of an inverse function can be different from the domain of the original function. This is because the inverse function may have different input values and output values than the original function.

4. What happens if the original function has a restricted domain?

If the original function has a restricted domain, the domain of the inverse function will also be restricted. This means that there will be certain input values that are not included in the domain of the inverse function.

5. How can I visually determine the domain of an inverse function?

You can visually determine the domain of an inverse function by graphing both the original function and its inverse on the same coordinate plane. The domain of the inverse function will be where the inverse function intersects the x-axis.

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