The Student Room Group
gf(x) = g(f(x))

f(x) = x^2 - 2ax
g(x) = 3ax
g(f(x)) = g(x^2 - 2ax)

g(x^2 - 2ax) = 3a(x^2 - 2ax)

3a(x^2 - 2ax) = 9a^3, and solve.
Reply 2
f(x) ≡ x^2 − 2ax
gf(x) = 3a(x^2 -2ax) = 9a^3
3x^2 - 6ax = 9a^2
3x^2 - 6ax - 9a^2 = 0

Now solve the quadratic using the formula to find x in terms of a.
Reply 3
Hello!

f(x) = x2 - 2ax
g(x) = 3ax

Find gf(x) = g(f(x))
gf(x) = g(x2 - 2ax)
gf(x) = 3a(x2 - 2ax)
gf(x) = 3ax2 - 6a2x = 9a3
3ax2 - 6a2x - 9a3 = 0
x2 - 2ax - 3a2 = 0

Use the quadratic formula to find x

x = (2 + or - ((4a2 - (4x-3a2) )0.5 ) /2
x = (2 + or - (16a2)0.5)/2
x = (2 + or - 4a)/2
x = 1 + 2a or x = 1-2a

love danniella