Question

Can someone PLEASE help I have tons of these problems and not even the slightest idea of how to do them?

1.Find f ○ g if g(x) = x + 1 and f(x) = 2x2 - 5x + 8

2.Find g ○ f if g(x) = x - 4 and f(x) = 3x2.

I MEAN WHAT DOES f o g EVEN MEAN?! I am a straight a student no where in my course do I recall this and he wont answer my emails so I'm at a total loss...
is it like f * g?????
like f times g?

Answer 1

Please see below.

Explanation:

.

`(f@g)(x)` is the same as `f(g(x))`.

If `f(x)=2x^2-5x+8` and `g(x)=x+1` then,

`(f@g)(x)=f(g(x))=2(x+1)^2-5(x+1)+8=2x^2+4x+2-5x-5+8=2x^2-x+5`

If `g(x)=x-4` and `f(x)=3x^2` then,

`(g@f)(x)=g(f(x))=3x^2-4`

It is ridiculous for your teacher to treat you this way. I hope this helps.

Answer 2

Below

Explanation:

`f ○ g` is just another way of writing `f(g(x))` or F of g of x it's very simple
For 1.Find f ○ g if g(x) = x + 1 and f(x) = 2x2 - 5x + 8 you have to plug `g(x)` into the `x` spot of `f(x)`
In other words:
`f(g(x))=2(x+1)2 - 5(x-1) + 8`
Honestly I would solve this for you but I don't know if that two after the the `x` means squared or multiply.