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Consider the following relation.

 

x = 2|y|− 3

 

Find the domain and range of the inverse. Express your answer in interval notation

 

Domain =                       Range =

 Nov 5, 2021
 #1
avatar+11 
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Find the domain and range of the inverse. Express your answer in interval notation

 

To find the inverse:

x=2y-3

x+3=2y

(x+3)/2=y

 

so the inverse of x=2y-3 is y=(x+3)/2

 

since the graph for this is just a just a line some degrees above the horizontal, the domain and range would be

 

Domain: {x|xER}        Range: {y|yER}

 Nov 5, 2021
 #2
avatar+115420 
+1

x = 2|y|− 3

 

Range is all real y

Domain is x>=3

 

So for the inverse:

Domain is all real x     (-infinty, infinty)

Range is y>=3            [-3,infinity)

 

check by graphing

The green one is the original and the purple one is the inverse  (reflection across y=x which is the red one)

 

 

 Nov 6, 2021

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