Question

Given that f(x) = –x + 4 and g(x) = –2x – 3, solve for f(g(x)) when x = 2.

Answer 1

@jdoe0001

Answer 2

\(\bf f(x)=-x+4\qquad {\color{brown}{ g(x)}}=-2x-3
\\ \quad \\
f(\quad {\color{brown}{ g(x)}}\quad )=-{\color{brown}{ g(x)}}+4\implies f(\quad {\color{brown}{ g(x)}}\quad )=-{\color{brown}{ (-2x-3)}}+4
\\ \quad \\
f(\quad {\color{brown}{ g({\color{blue}{ 2}})}}\quad )=-{\color{brown}{ (-2({\color{blue}{ 2}})-3)}}+4\)

Answer 3

I'm still lost... this is my first day of Algebra 2.

Answer 4

f( g(x) )

means, "replace any "x" variable in f(x), with g(x)"

notice how the g(x) takes over the "x" in f(x)

Answer 5

for example if say g(x) = ducks

then f( g(x) ) = -(ducks) + 4
^
used to be x

Answer 6

So do I just plug in 2 somewhere?

Answer 7

well... first you expand the f( g(x) )
and then plug in the "2"

Answer 8

Ahhh I'm really struggling here.

Answer 9

f( something ) = -"something" + 4

f( pelicans ) = -"pelicans" + 4

f( albatross ) = - "albatross" + 4

"x" is just a variable, it coiuld be anything, it just so happen that's "x"

but whatever f( "show here" ) <-- will be the variable used in it

Answer 10

Ohh.

Answer 11

say for example \(\bf f(x) = 2x+3x^2\qquad g(x)=pelicans
\\ \quad \\
f(\quad g(x)\quad ) \iff f(pelicans)=2(pelicans)+3(pelicans)^2\)

Answer 12

Ah okay!

Answer 13

(Still a bit confused but I'm starting to get it)

Answer 14

How would this information help me create a solution?

Answer 15

well... notice how g(x) gets inserted firstly
and then
how the "2" gets inserted secondly \(\bf f(x)=-x+4\qquad {\color{brown}{ g(x)}}=-2x-3
\\ \quad \\
f(\quad {\color{brown}{ g(x)}}\quad )=-{\color{brown}{ g(x)}}+4\implies f(\quad {\color{brown}{ g(x)}}\quad )=-{\color{brown}{ (-2x-3)}}+4
\\ \quad \\
f(\quad {\color{brown}{ g({\color{blue}{ 2}})}}\quad )=-{\color{brown}{ (-2({\color{blue}{ 2}})-3)}}+4\)

Answer 16

I got 11.

Answer 17

yeap

Answer 18

..OH!

Answer 19

Thank you so much!

Answer 20

yw

Answer 21

Would you mind doing one more? It's a fraction one.

Answer 22

easier if you post anew, sure... that way if I dunno, someone else may

Answer 23

Posted!