Question

Which expression represents the composition [f o g o h](x) for the functions below?

f(x) = –2x4
g(x) = 4x – 6
h(x) = x – 1

Answer 1

I think it's -2(4x-10)^4, but I wanted to check.

Answer 2

@Directrix

Answer 3

Let's work from the inside out.

f(x) = –2x4

g(x) = 4x – 6

h(x) = x – 1

g of h(x) = g (x - 1) = 4* (x - 1) - 6 = 4x - 10

So, g(h(x)) = 4x - 10

and then ...

Answer 4

f(x) = –2x4

f(4x - 10) = -2 * (4x - 10)^4 = ?

*That will be f(g(h(x))) = -2 * (4x - 10)^4 *

I don't know if you are required to expand that.

Answer 5

Nope, I'm not required to expand that. Thank you!
I was wondering if you could clear up something for me?

g(f(x))=[gof](x)

Is this correct?

Answer 6

-2(4x-10)^4 is what you got which is what I got.

This website is rocking and rolling like a ship in a tempest.

Answer 7

I don't use the circle notation myself because I have to think of the composition in a "layers of an onion" mindset.

I would like to say that it is correct to write it that way but I cannot say so with certainty. Sorry.

Answer 8

Ok, thank you. I've always used g(f(x)), but the algebra class I'm taking has been using the other way I showed you and I wasn't sure if it actually was another way to write it or if I was getting something mixed up.

Answer 9

The way the class is using the notation is easier on the eyes.

Answer 10

Ah, I suppose. I'd better get on with my homework, considering I have a huge history test on Friday. Thank you for helping me! :)

Answer 11

[f o g o h](x)

To keep the order of the composition straight in my head, I tend to use this nest:
f(g(h(x)))

Answer 12

You are welcome.