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If \(f(x)=\dfrac{a}{x+2}\) , solve for the value of \(a\) so that \(f(0)=f^{-1}(3a).\)

 Feb 17, 2019
edited by Guest  Feb 17, 2019
edited by Guest  Feb 17, 2019
edited by Guest  Feb 17, 2019
 #1
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please help anyone???

 Feb 17, 2019
 #2
avatar+192 
+2

Hey there guest.

f(0)=a/2

note that f^-1 is the recipricol of f

knowing that, f(3a)=a/3a+2. f^-1(3a)= 3a+2/a

 

f(0)=f^-1, so a/2=3a+2/a. Cross multiplying gives a^2=6a+4

a^2-6a-4=0

 

Completing the square time:

a^2-6a+9=13

(a-3)^2=13

a-3=+/-sqrt13

a=+/-sqrt3 + 3

Hope this helps

 Feb 17, 2019
 #3
avatar+27544 
+1

f-1 means inverse rather than reciprocal, so if f(x) = a/(x+2) then f-1(x) = a/x - 2

 

f(0) = a/2

f-1(3a) = 1/3 - 2 = -5/3

 

So a/2 = -5/3 or a = -10/3

 Feb 17, 2019

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