# 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 - 3` , you should substitute g(x) for x such that:

`f(g(x)) = 2g(x) - 3`

The problem provides the information that `f(g(x)) = 2x+1` , hence, you should set the equations 2g(x) - 3 and 2x+1 equal such that:

`2g(x) - 3 = 2x + 1 =gt 2g(x) = 2x + 1 + 3`

`2g(x) = 2x + 4`

Dividing by 2 yields:

`g(x) = x + 2`

**Hence, evaluating the function g(x) under the given conditions yields `g(x) = x + 2` .**

**Sources:**

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