# If f(x)=2x+1 and g(f(x))=4x^2+4x+3 find g(x) given that g(x)=ax^2+bx+c how do I do that?

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I know that somebody has solved this before but I would like a better version of that one since I did not understand what was going on in the other one. Many thanks!

I know that somebody has solved this before but I would like a better version of that one since I did not understand what was going on in the other one. Many thanks!

##### 1 Answer

#### Explanation:

We know that

Expanding the parentheses:

Rearranging the variables:

Now, we are also given the fact that

Comparing coefficients:

Therefore,