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f(x) = ax+b, 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?

 Apr 19, 2022
 #1
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g(f(x))  =  2(f(x))  -  5  =  2(ax + b) - 5  =  2ax + 2b  - 5

 

Compare coefficients of x with 3x + 4  

 

so  2a = 3

and 2b - 5 = 4

 

I'll leave you to complete this.

 Apr 19, 2022

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