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Let  \(f(x) = ax+b\) , where \(a\) and \(b\) are real constants, and \(g(x) = 2x - 5\) . Suppose that for all \(x\) , it is true that \(g(f(x)) = 3x + 4\). What is \(a+b\)?

 Oct 30, 2019
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g(f (x) ) =   2(ax+b) -5     for all x , this equals 3x+4    solve for a and b

2ax+2b - 5 = 3x+4

2ax = 3x     and   2b-5 = 4

a = 3/2       and  b = 9/2           I think you can add these together for the answer....   cheeky

 Oct 30, 2019

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