Question

The function g(x)=x^2+3. The f(x)=g(x+2)

Answer 1

Answer:

$f(x)=x^2+6x+12$

Step-by-step explanation:

Given:

The function 'g(x)' is given as:

$g(x)=x^2+3$

Now, the function 'f(x)' is given as:

$f(x)=g(x+2)$

So, the function 'f(x)' is a transformation of 'g(x)'.

In order to find f(x), we replace 'x' by $(x + 2)$ in the 'g(x)' function equation. This gives,

$g(x+2)=(x+2)^2+3$

Using the identity $(a+b)^2=a^2+b^2+2ab$, we get:

$g(x+2)=x^2+3^2+6x+3\\\\g(x+2)=x^2+9+6x+3\\\\g(x+2)=x^2+6x+12$

Hence the function f(x) is given as:

$f(x)=x^2+6x+12$