Question

Given f(x) = 2x + 3 and ( f o g)(x) = –2x^2 + 13. find g(x)?

Answer 1

well, 2g + 3 = -2x^2 +13, solve for g

Answer 2

why did the x in f(x) become g?

Answer 3

because of the notation:

(fog)(x) = f(g(x)) so we simply let all x in f be the value of g

Answer 4

(fog) = f(g)

since f(x) = 2x + 3, when x=g we have: f(g) = 2g + 3

Answer 5

ohhh ok, but what if its the other way around?

Answer 6

it's just the same? the x in g(x) will become f?

Answer 7

you mean g(f) is equal to some function?

Answer 8

if we want to determine (gof) then yes we let all x in g be equal to f

Answer 9

I solved the problem and got g(x) = –x^2 + 5 . I was just wondering if you could pretend to not know the value of f(x) and solve for the f(x)

Answer 10

that's -x^2+5

Answer 11

if we were given g(x) = -x^2 + 5, and (fog)(x) = -2x^2 + 13, and find f(x) ?

Answer 12

yes

Answer 13

since we have no f to place g into, it gets trickier and not as precise.

we know we need a -2x^2 so multiplying by -2 is a good step to take

-2g = -2x^2 + 10

we know we want a +13 so we need to add in 3

-2g + 3 = -2x^2 + 13

and we have a construction that matches now so we we let all g in f be equal to x to determine f(x)

Answer 14

and i seem to have forgotten the we had a -x^2 up from to start with ... so the steps i thought of arent accurate for that one

Answer 15

ohh you're a math genius

Answer 16

sometimes, other times im just a math idiot :)

Answer 17

thanks I understood it

Answer 18

good luck ;)