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The graphs of a function \(f(x)=3x+b\) and its inverse function \(f^{-1}(x)\) intersect at the point \((-3,a)\) . Given that b and a are both integers, what is the value of  \(a\)?

tertre  Mar 14, 2017
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 #1
avatar+76929 
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The inverse function is

 

y = [x - b] / 3 

           

Set these functions equal

 

3x + b  =  [x - b]/ 3

 

9x + 3b   = x - b

 

8x  = -4b

 

b = -2x

 

So...using the first function

 

y = 3x - 2x

 

a = 3(-3) - 2(-3)

 

a = -9 + 6

 

a = -3         and   b  = -2(-3) =  6

 

Check

 

y = 3(x) + 6             and      y  =   [ x  - 6 ] / 3

a = 3(-3) + 6                       -3  = [ a  - 6] / 3 

a = -3                                 -3  = [ -3 - 6] / 3

                                          -3  = [-9] / 3

                                           -3  = -3            

 

So....the intersection point is (-3, -3)

 

See the graph here : https://www.desmos.com/calculator/r2jbhnwsj2

 

 

 cool cool cool

CPhill  Mar 14, 2017

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