+136 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
+6248 \((f\circ g)(x) = f(g(x))\\ -\\ \begin{matrix} x &g(x) &f(g(x)) \\ 0 &4 &-6\\ 1 &3 &13 \\ \vdots \end{matrix}\\ \text{see how it works?}\)
.
+128407 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 ???
+128407 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
