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KiRa [710]
2 years ago
10

Please help asap find f -1

Mathematics
1 answer:
ExtremeBDS [4]2 years ago
8 0
I.
Given a function f with domain D and range R, and the inverse function 
f ^{-1},

then the domain of f ^{-1} is the range of f, and the range of f ^{-1} is the domain of f.

II. We are given the function f(x)= \sqrt{x-5},

the domain of f, is the set of all x for which \sqrt{x-5} makes sense, so x is any x for which x-5\geq0, 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 f ^{-1} is [0, ∞) and the Range of f ^{-1} is [5, ∞) 

III.
Consider f(x)= \sqrt{x-5}

to find the inverse function f^{-1}, 

1. write f(x) as y:

y= \sqrt{x-5}

2. write x in terms of y:

y= \sqrt{x-5}

take the square of both sides

y^{2} =x-5

add 5 to both sides

y^{2} +5=x

x=y^{2} +5

3. substitute y with x, and x with f^{-1}(x):

f^{-1}(x)=x^{2} +5


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

IV. Answer: 

f^{-1}(x)=x^{2} +5, x≥0

y≥0, where y are all the values that f^{-1} can take

Remark: the closest choice is B

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