Answer:
[tex]f(x)=x^2+6x+12[/tex]
Step-by-step explanation:
Given:
The function 'g(x)' is given as:
[tex]g(x)=x^2+3[/tex]
Now, the function 'f(x)' is given as:
[tex]f(x)=g(x+2)[/tex]
So, the function 'f(x)' is a transformation of 'g(x)'.
In order to find f(x), we replace 'x' by [tex](x + 2)[/tex] in the 'g(x)' function equation. This gives,
[tex]g(x+2)=(x+2)^2+3[/tex]
Using the identity [tex](a+b)^2=a^2+b^2+2ab[/tex], we get:
[tex]g(x+2)=x^2+3^2+6x+3\\\\g(x+2)=x^2+9+6x+3\\\\g(x+2)=x^2+6x+12[/tex]
Hence the function f(x) is given as:
[tex]f(x)=x^2+6x+12[/tex]
