Find the inverse of the function on the given domainf(x)=(x−10)2,[10,∞)f−1(x)= .....Note: There is a sample student explantion given in the feedback to this question.

Step 1f(x)={({x−10})2},[{10,∞})Replace f(x) with yy=(x−10)2Interchange x and y x=(y−10)2Take the square root±x()=y−10Add 4 to each side10±x()=yRename the function f−1(x){f−1}(x)=10±x()Domain [10,∞), so f−1(x)=10+x()

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High School
Algebra
Algebra I
Quadratic function and equation

Haylee Bowen

Answered question

2022-04-14

Find the inverse of the function on the given domain

f (x) = {(x - 10)}^{2}, [10, \infty)

f^{- 1} (x) =

.....
Note: There is a sample student explantion given in the feedback to this question.

Answer & Explanation

mislifola5vo

Beginner2022-04-15Added 11 answers

Step 1
Take the given function as equal to y the and d find value of x in terms of y.
Step 2

f (x) = {(x - 10)}^{2} [10, \infty)

Ifence

y = {(x - 10)}^{2}

\Rightarrow (x - 10) = \sqrt[()]{y}

\Rightarrow x - (\sqrt[()]{y} + 10)

Hence

f^{- 1} (x) = (\sqrt[()]{x} + 10)

calcinaretnbz

Beginner2022-04-16Added 5 answers

Step 1

f (x) = {{({x - 10})}^{2}}, [{10, \infty})

Replace

f (x)

with y

y = {(x - 10)}^{2}

Interchange x and y

x = {(y - 10)}^{2}

Take the square root

\pm \sqrt[()]{x} = y - 10

Add 4 to each side

10 \pm \sqrt[()]{x} = y

Rename the function

f^{- 1} (x)

{f^{- 1}} (x) = 10 \pm \sqrt[()]{x}

Domain

[10, \infty)

, so

f^{- 1} (x) = 10 + \sqrt[()]{x}

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