QuestionFind the inverse of the one-to-one function . What is ?
Studdy Solution
STEP 1
Assumptions1. The function is one-to-one, which means that for every there is a unique and vice versa. . We are given the function and we need to find its inverse .
STEP 2
To find the inverse of a function, we first replace with .
STEP 3
The next step to find the inverse of a function is to swap and . This means we replace with and with .
STEP 4
Now, we need to solve this equation for to find the inverse function.
First, add to both sides of the equation to isolate the term with .
STEP 5
Finally, divide both sides of the equation by2 to solve for .
STEP 6
Now that we have solved for , we can write the inverse function. We replace with to denote the inverse function.
So, the inverse of the function is .
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