Question

Hello I really need help, like ASAP. I am not getting this at all.

The function that I used.
f(x)= 2x + 8

6. The Martians ask you to explain one last thing, Ultimate Math Ambassador. They ask you to create a new function, h(x). Then assign any number to x. Using complete sentences, explain whether f(h(x)) and h(f(x)) will always result in the same number. You will use the function f(x) that you created in problem number 2.

Answer 1

Okay, you used \[f(x) = 2x+8\]You need to make up another function, \(h(x) = \) (whatever you chose)
Let's say you used \[h(x) = 3x\]

Make a table:

x f(x) h(x) f(h(x)) h(f(x))
0 8 0
1 10 3
2 12 6

I haven't filled in the columns for \(f(h(x))\) and \(h(f(x))\); that's for you to do. With your formula for \(f(x)\) and mine for \(h(x)\), here's how you would calculate them:

\[f(0) = 2(0)+8 = 0+8 = 8\]\[h(0) = 3(0) = 0\]\[f(h(0)) = f(3(0)) = f(0) = 2(0)+8 = 8\]\[h(f(0)) = h(2(0)+8) = h(8) =\]

Answer 2

I don't get the f(h(x)) and h(f(x)) part... like what does that mean?

Answer 3

@whpalmer4

Answer 4

\[f(h(x))\]means evaluate \(h(x)\) at some value of \(x\), then take the result, and use it as \(x\) in evaluating \(f(x)\).

So if \(h(3) = 7\), then \(f(h(3)) = f(7) = \)

Does that make sense? It's a bit confusing because \(x\) gets reused and may have a different value...