Given that f(0)=−7, f(1)=−9, f(2)=16 f(3)=13, f(4)=−6,

and g(0)=4, g(1)=3, g(2)=0, g(3)=2, g(4)=1,

evaluate the following:

(a) (f∘g)(0)=

(b) (f∘g)(1)=

(c) (f∘g)(2)=

(d) (f∘g)(3)=

(e) (f∘g)(4)=

Please help, I've been trying at it for hours and I still can't wrap my head around it, and if possible, please explain how you got to the answer? I really want to learn this well, as I feel that I'm doing one step incorrectly and therefore the whole thing is wrong

Roxettna Feb 19, 2019

#1**+4 **

\((f\circ g)(x) = f(g(x))\\ -\\ \begin{matrix} x &g(x) &f(g(x)) \\ 0 &4 &-6\\ 1 &3 &13 \\ \vdots \end{matrix}\\ \text{see how it works?}\)

.Rom Feb 19, 2019

#2**+5 **

The notation is probably what is giving you trouble

( f ° g) (0) means this ⇒ f ( g(0) )

We first evaluate g(0) = 4

So...now we have

f ( g(0) ) = f(4) = -6

Another way to see this is to work from right to left

So put 0 into g and we get g(0) = 4

Then...put this into f and we have f(4) = -6

Does that make sense ???

CPhill Feb 19, 2019

#3**+5 **

Let's look at (d) for another example

(f ° g ) (3)

We put 3 into g and get g(3) = 2

Then...we put this result into f and get f(2) = 16

CPhill Feb 19, 2019