Answer:
4th choice
Step-by-step explanation:
<u>Definition of the inverse of a function</u>
A function g is the inverse of a function f if whenever y=f(x) then x=g(y). In other words, applying f and then g is the same thing as doing nothing. We can write this in terms of the composition of f and g as g(f(x))=x. The domain of f becomes the range of g and the range of f becomes the domain of g
To solve for the inverse of the function
Let
Switch sides
Take square roots on both sides
Add 4 on both sides to solve for y
We have two solutions
To determine which one of these to be chosen not that in the given choices we can eliminate the first two since x cannot be negative
The third choice can also be eliminated since is a decreasing function for
So the last answer choice is correct and the inverse of
is given by
Answer:4th choice
Note
Domain of (x-4)² is [4, ∞) since x ≥ 4 and (x-4)² cannot be negative
Range of (x-4)² is [0, ∞)
Domain of is [0, ∞)
Range of is [4, ∞)
so indeed the domain of (x-4)² has become the range of and the range of (x-4)² has become the domain of
