## anonymous one year ago Write the equation of the function g(x) if g(x) = f(x – 2) +4 and f(x) = x^3 + 2. I already took the test that had this question, I just want to know how to solve it, please. I feel like it may be such an easy question, but I'm just overthinking it.

1. Nnesha

find f(x-2) first replace x with x-2 into f(x) function

2. Nnesha

$\huge\rm f(\color{ReD}{x-2})=\color{ReD}{x}^3+2$ ^^replace x with x-2

3. Nnesha

then solve right side you can apply the foil method or remember $\huge\rm \rm (a+b)^3=a^3+3a^2b+3ab^2+b^3$ any question ? feel free to tag my name!

4. anonymous

And that should give me g(x)? @Nnesha

5. Nnesha

no that would you give you f(x-2)

6. Nnesha

$\huge\rm g(x)= \color{ReD}{f(x-2)}+4$ so then you can substitutef(x-2) with the result

7. Hero

@Nnesha, $$f(x - 2) = (x - 2)^3 + 2$$

8. anonymous

OOHHH okay I got you, that makes so much more sense. I was completely thinking about it in a different way. I know how to do it now. Sorry about that. Thanks:) @Nnesha

9. Nnesha

correction (a-b)^3 ** $\large\rm \rm (a-b)^3=a^3-3a^2b+3ab^2-b^3$

10. Nnesha

$$\color{blue}{\text{Originally Posted by}}$$ @Hero @Nnesha, $$f(x - 2) = (x - 2)^3 + 2$$ $$\color{blue}{\text{End of Quote}}$$ yes, i wanted him to substitute 2nd x