Question

Let f(x) = ax^2 and g(x) = bx + c, where a, b, and c are constants.
Compute f (g(x)) and g (f(x)). Determine for which constants a, b, and c it
is true that f ( g(x)) = g(f(x))

Answer 1

I know how to get f(g(x)) I got a(bx+c)^2 and g(f(x))=b(ax^2)+c but when I made them equal

Answer 2

I can't solve for anything

Answer 3

expanding to get b^2x^2+2bx +c^2=abx^2+c if they are equal

Answer 4

so b^2=ab
b^2-ab=0
b(b-a)= 0
b=0 b=a

Answer 5

oops made an error

Answer 6

a(b^2x^2+2bx +c^2)=abx^2+c

Answer 7

ab^2=ab
ab^2-ab=0
ab(b-1) = 0 so b = 1

Answer 8

sorry I don't see how you got that ab^2=ab from the equation?

Answer 9

with the x terms 2ab =0 hmm with the constants ac^2 = c

ac^2 - c = 0
c(ac -1)= 0

Answer 10

I equated the coefficients

Answer 11

equate the coefficients on the left from f(g(x)) and g(f(x)) ... I used what u said u got

Answer 12

oh so then 2abx=0 and c^a=c?

Answer 13

oops c^2a=c

Answer 14

if they are equal then the coefficients of x^2, x and the constants must be equal ... hope that helps

Answer 15

That make sense then you just leave them like that? you can't really get actually values