Question

Let f(x) = 3x+2 and g(x) = x^2

Part 1 [2 points] Find f(g(x))
Part 2 [2 points] Find g(f(x))
Part 3 [4 points] Use complete sentences to explain any difference in part 1 and part 2.

Answer 1

@phi

Answer 2

@amistre64

Answer 3

@Mandre

Answer 4

@cwrw238

Answer 5

f(g(x))=3x^2+2

Answer 6

How do I solve this?

Answer 7

Find f(g(x)) means start with f(x) = 3x+2
replace x with g(x): erase the x, and put in g(x)
f(g(x))= 3g(x) + 2

but g(x) is x^2
so replace g(x) with x^2 :
f(g(x))= 3x^2 +2

Answer 8

Okay, does that get simplified?

Answer 9

Is that the final answer?

Answer 10

you can't do anything with 3x^2+2
there are no *like terms*

Answer 11

Okay, what about part 2?

Answer 12

now try
g(f(x))

start with g(x) = x^2

Answer 13

I don't know...

Answer 14

@phi I don't get it

Answer 15

you want
g(f(x))
which is short for "start with g(x)" and replace x with f(x)"

g(x) = x^2

if you erase the x, and put in f(x) (in other words, put in "f(x)" ) what do you get ?

Answer 16

(3x+2)^2?

Answer 17

yes

Answer 18

Okay, how do I do part 3? What's different? g(f(x)) is just f(x) squared?

Answer 19

if we expand g(f(x))= (3x+2)^2= 9x^2 +6x+4
and compare to
f(g(x))= 3x^2+2

they are both quadratics, by g(f(x)) is "bigger" because of the 9x^2 instead of the 3x^2