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# Mathtertre

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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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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

CPhill  Mar 14, 2017

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