if f(x)=2x-3 and fg(x)=2x+1,find g(x)

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You should notice that the composition of the functions f and g is a linear function.

You need to remember how to compose two functions such that:

`(fog)(x) = f(g(x))`

Since `f(x) = 2x -...

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dodafone | Student

first we see that g(x) should be a linear polynomial as only then fg(x) will come out to be linear 

let g(x)=ax + b

fg(x)=2(ax +b) -3

=x(2a) +(2b-3) which is given equal to 2x +1

on comparing we get 
2a=2        a=1

2b-3=1     b=2

g(x)=x+2

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