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

 Jun 19, 2019
 #1
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f(x)  = ax +b

 

g(x)  =  2x - 5

 

g(f(x))  =  3x + 4

 

So....we have that

 

2 ( ax + b) - 5   =   3x + 4

 

2ax + 2b - 5  =  3x + 4

 

So....equating coefficients

 

2a  = 3         and        2b - 5  = 4

a = 3/2                        2b = 9

                                     b = 9/2

 

So

 

a + b   =  (3/2) + (9/2)  =  12 / 2    =   6

 

 

 

cool cool cool

 Jun 19, 2019

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