Which one is a counter example?
2 answers:
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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-5
0, 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. Answer:
, x≥0
y≥0, where y are all the values that
can take
Remark: the closest choice is B
Given a function f with domain D and range R, and the inverse function
then the domain of
II. We are given the function
the domain of f, is the set of all x for which
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
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. Answer:
y≥0, where y are all the values that
Remark: the closest choice is B