Question

Write the equation of the function g(x) if g(x) = f(x – 2) +4 and f(x) = x3 + 2.

Answer 1

First, a little housekeeping: x3 is ambiguous; I believe you mean "the cube of x," which should be written x^3.

Answer 2

Oh yes, I meant that. My bad

Answer 3

Write the equation of the function g(x) if g(x) = f(x – 2) +4 and f(x) = x^3 + 2.

Step 1: replace "x" in f(x) = 2^3 +2 with (x-2). Example: f(x) becomes f(x-2).

Answer 4

What do you get? f(x-2)= ??

Answer 5

f(x-2) = 10?

Answer 6

First, f(x) = x^3 + 2.
Replace each 'x' with (x-2): f(x-2)=(x-2)^3 + 2. Simplify this if possible (it may not be possible).

Answer 7

The problem defines g(x) as f(x-2). So, without doing any more, you could write
g(x)=f(x-2)=(x-2)^3+2. OK with that?

Answer 8

Yes, okay with that

Answer 9

The problem defines g(x) as f(x-2) + 4. So, without doing any more, you could write
g(x)=f(x-2)=(x-2)^3+2+4. OK with that?

Answer 10

Yes

Answer 11

So would g(x) = f(x-2) = (x-2)^3+6 be the final answer?

Answer 12

Yes. Very good. Any questions about this process?

Answer 13

No, thank you!

Answer 14

Great pleasure. Take caer!