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If h(y) = (1 + y)/(2 + y), then what is the value of $h^{-1}(5)$? Express your answer in simplest form.

 Apr 22, 2021
 #1
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+1

ElictricPavlov already answered this but this is what he said "

X = (y+1)/(y+2)   to get the inverse, switch x's and y 's then solve for x

y = (x+1)/(x+2)

(x+2)y =  x+1

xy + 2y -x = 1

x ( y-1) = 1 - 2y

x = (1-2y)/(y-1)       is the inverse       h-1 (5) = -9/4  =  - 2 1/4

"

 Apr 22, 2021
 #2
avatar+121048 
+1

(y, 5)  is  on  the original function

 

So   (5, y)  is  on the  inverse

 

So  ....We  can solve this

 

5  =  (1 + y)  / (2 + y)

 

5 (2 + y)  =  1 + y

 

10  + 5y  =  1 + y

 

5y - y =  1  -10

 

4y  = -9

 

y  = -9/4  =  h-1(5)

 

 

cool cool cool

 Apr 22, 2021

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