Asap find f -1
(picture of equation below)

a. f­-1 (x) = x2 +25; y> 25
b. f ­-1 (x) = x2 + 5; y > 5
c. f ­-1 (x) = (x + 5)2; y > 5
d. f­-1 (x) = x2 +25; y> 5

I.
Given a function f with domain D and range R, and the inverse function 
,

then the domain of is the range of f, and the range of is the domain of f.

II. We are given the function ,

the domain of f, is the set of all x for which makes sense, so x is any x for which x-50, that is x≥5.

the range is the set of all values that f can take. Since f is a radical function, it never produces negative values, in fact in can produce any value ≥0

Thus the Domain of f is [5, ∞) and the Range is [0, ∞)
then , the Domain of  is [0, ∞) and the Range of is [5, ∞) 

III.
Consider

to find the inverse function , 

1. write f(x) as y:



2. write x in terms of y:



take the square of both sides



add 5 to both sides





3. substitute y with x, and x with :



These steps can be applied any time we want to find the inverse function.

IV.  

, x≥0

y≥0, where y are all the values that can take

Remark: the closest choice is B

In all honesty, there really is no “work” per say to show. mainly it’s just using the process of elimination. the question is asking which domain(s) would be the most appropriate for the function c(n). n is the number of observed vehicles so right away, 1, 2, and 3 can be eliminated.why? 1, 2 start in the negatives and therefore it is impossible to observe negative cars. so, #4 would be the best answer to the given problem.