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How does a domain restriction placed on a non-invertible function affect its inverse?

Drag a function or an interval into each box to correctly complete the statement.

When the domain of the non-invertible function f(x)=(x+1)^2 − 3 is [−1,∞), the inverse of the function is f^−1(x) = x+3 -1, and the domain of the inverse function is [3, ∞).

 

my answers are bolded. they are correct?? thx !!

 Jan 15, 2021
 #1
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Note  that  in the origial function  f(-1) =  -3   .....the point  (-1,-3)   is on the graph of the original

 

So....the point  (-3, -1)  is on the inverse

 

Find the inverse

 

y =   ( x + 1)^2  - 3

 

y + 3  =  ( x + 1)^2       take the positive root

 

sqrt ( y + 3)  = x + 1      subtact 1 from both sides

 

 sqrt (y+ 3)  - 1  =  x       "swap"  x and y

 

y =  sqrt (x + 3)  - 1   =  the inverse

 

Note that (-3,-1)  is on the  graph

 

And the  domain is   [ -3, inf )

 

See the graph here : https://www.desmos.com/calculator/kjrdf25ehj

 

cool cool cool

 Jan 15, 2021

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