Question

Given f(x)=x^2+1,fg(x)=x^2+4x+5
Find the function of g.
@mathmath333

Answer 1

\[x^2(g(x))+1=x^2+4x+5\]

Answer 2

separate your 5 \[fog(x)=(x^2+4x+4)+1\]

Answer 3

ok

Answer 4

\[fog(x)=f(g(x))\]It's a way of representing composite functions
All I did was separate your 5 into 4 and 1
\[fog(x)=f(g(x)=x^2+4x+4+1\]

Answer 5

okay

Answer 6

Now we must substitute f(x)=x^2+1 ?

Answer 7

that is not needed really just notice your first 3 terms, they form an identity

Answer 8

pleasenote that we can write:
\[f\left( {g\left( x \right)} \right) = {\left( {g\left( x \right)} \right)^2} + 1\]

Answer 9

furthermore, we have:
\[{x^2} + 4x + 5 = {x^2} + 4x + 4 + 1 = {\left( {x + 2} \right)^2} + 1\]

Answer 10

nemely:
\[f\left( {g\left( x \right)} \right) = {x^2} + 4x + 5 = {x^2} + 4x + 4 + 1 = {\left( {x + 2} \right)^2} + 1\]

Answer 11

so the function of g is
g(x)=x+2?

Answer 12

that's right!

Answer 13

Thnx @Michele_Laino and Nishant_Garg

Answer 14

thanks! @MARC_