Question

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.

Answer 1

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

Answer 2

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

Answer 3

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!

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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