Question

I'm doing a worksheet for algebra II, and I need some help with a concept.

Here's the question and my work:
Create a new function, h(x). Then assign any number to x. Using complete sentences, explain whether f(h(x)) and h(f(x)) will always result in the same number. You will use the function f(x) that you created in problem number 2. f(x) = x^2 + 2 and h(x) 2x – 4. Let x equal 6.
h(x) = 2(6) – 4
f(h(x)) = (2(6) – 4)^2 + 2
f(h(x)) = (12 – 4)^2 + 2
f(h(x)) = 8^2 + 2
f(h(x)) = 64 + 2 = 66
h(f(x)) = 2(6^2 + 2) – 4
h(f(x)) = 2(36 + 2) – 4
h(f(x)) = 76 – 4
h(f(x)) = 72

Answer 1

So my question is - SHOULD those be getting the same answer?

Answer 2

Is there something I need to change in my approach to get the same answers?

Answer 3

@random231 Can you help again?

Answer 4

@brandonE

Answer 5

in general, \[f ° g \neq g°f\] . Remember that the notation
f g means that the function g is applied first and then f is applied second.

Answer 6

@rock_mit182 It's not supposed to be equal?

Answer 7

in general is supposed, cause is no commutative ( like in sum,3+5=5+3) in this case the order matters

Answer 8

besides their domains can differ

Answer 9

Okay. Thank you :)

Answer 10

Did I get the order right in applying f(x) first?

Answer 11

@rock_mit182

Answer 12

sure your work is clear

Answer 13

f ° g = f (g(x)) ;
g ° f = g (f(x) ;

Answer 14

yeah good job ;)

Answer 15

@random231 Can you help me once more w/ inverse functions? f(x) = x^2 + 2 when f(x) = 3.

Answer 16

Thank you! Thanks for your help :)

Answer 17

ya sure!!

Answer 18

@random231 x = y^2 + 2...do I substitute 3 for y?

Answer 19

yeah but you halve to solve for y then

Answer 20

have*

Answer 21

exactly!
actually when u find the inverse of a function and write it as a function of x,JUST SUBSTITUTE Y WITH X.

Answer 22

then plug the value 3

Answer 23

yup!

Answer 24

Okay, could you write out what that would look like? I'm a little confused, sorry :( Well, not confused, but I need a visual.