QuestionFind a domain for that makes it one-to-one and non-decreasing. Determine the inverse .
Studdy Solution
STEP 1
Assumptions1. The function is . We need to find a domain on which is one-to-one and non-decreasing3. We need to find the inverse of restricted to this domain
STEP 2
The function is a parabola opening upwards. It is symmetric about the line . To make it one-to-one and non-decreasing, we should restrict the domain to .
STEP 3
Now, let's find the inverse of restricted to this domain. The inverse of a function is denoted by and it undoes the operation of .To find the inverse, we first replace with .
STEP 4
Next, we swap and to get the equation in terms of .
STEP 5
To solve for , we take the square root of both sides. But since we are only considering the domain , we only take the positive square root.
STEP 6
So, the inverse of restricted to the domain is .
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