Question

Suppose that the functions and are defined as follows

see pic

Find the following.

Answer 1

@jigglypuff314 can you help me

Answer 2

(not completely sure?) would you plug in?

(r * q)(-1) = (-1)(x^2 + 2)(-2x) then distribute?
= 2x(x^2 + 2)
=

Answer 3

2x^3+4x?

Answer 4

I think so :)

Answer 5

or not... >,<
I feel like I'm doing something wrong

Answer 6

I haven't done this topic in a looonnnggg time...
is this when (r o q) means r(g(x)) ?

Answer 7

yes

Answer 8

gosh darn...
then does the (-1) after it mean multiply by negative or does it mean inverse?
idk XD

Answer 9

idk either.

Answer 10

I has brain fart .-.
help?
@jdoe0001 @mathmale @uri

Answer 11

\(\bf {\color{red}{ q}}(x)=-2x\qquad {\color{blue}{ r}}(x)=x^2+2\\ \quad \\
(r\ o \ q)\implies r(\quad q(x)\quad )=({\color{red}{ -2x}})^2+2\\ \quad \\
(q\ o \ r)\implies q(\quad r(x)\quad )=-2({\color{blue}{ x^2+2}})\)

Answer 12

yeah but what does the (-1) part of (r o q)(-1)
do to it?

Answer 13

it just replaces the "x" argument

Answer 14

\(\bf {\color{red}{ q}}(x)=-2x\qquad {\color{blue}{ r}}(x)=x^2+2\\ \quad \\
(r\ o \ q)\implies r(\quad q(x)\quad )=({\color{red}{ -2x}})^2+2\\ \quad \\

(q\ o \ r)\implies q(\quad r(x)\quad )=-2({\color{blue}{ x^2+2}})\\ \quad \\

(r\ o \ q)(-1)\implies r(\quad q(-1)\quad )=({\color{red}{ -2(-1)}})^2+2\\ \quad \\

(q\ o \ r)(-1)\implies q(\quad r(-1)\quad )=-2({\color{blue}{ (-1)^2+2}})\)

Answer 15

ohhhh okay :) thanks

Answer 16

yw

Answer 17

yes thank you both

Answer 18

r o q= 6
q o r= -6?

Answer 19

mmm yeah :)

Answer 20

In case anyone is interested: the topic here is "composite functions" or just "composites."\[(f o g)(x)\] does imply that g(x) is the input to the function f(x).

If q=-2x and r=x^2 + 2, then
\[(r o q)(x) = (-2x)^{2}+2\] = (4x)^2 + 2
and if x=-1, (r o q)(-1)=(-2*[-1])^2 +2=4+2=6.