Posted by Saud on Wednesday, November 21, 2012 at 11:44am.
Thanks steve for a brilliant answer! Got one last one which is gobbledegook to me.
Two functions f and g are defined by
f:x(arrow)x^2 + 3
g:x(arrow)2x + 1
find:
a) the function fg
b)solve the equation f(x) = 12g^1(x)
Many Thanks!!!!

Maths  Steve, Wednesday, November 21, 2012 at 12:37pm
using the usual notation,
f(x) = x^2+3
g(x) = 2x+1
fg = f(x)*g(x) = (x^2+3)(2x+1) = 2x^3 + x^2 + 6x + 3
f(x) = 12g^1(x)
g^1(x) = (x1)/2
so, solve x^2+3 = 12(x1)/2
x^2+3 = 6x6
x^2  6x + 9 = 0
(x3)^2 = 0
x = 3

Maths  Steve, Wednesday, November 21, 2012 at 12:39pm
If by fg you meant f◦g (that is, f(g(x))), then
since f(x) = x^2+3,
f(g) = g^2+3 = (2x+1)^2+3 = 4x^2 + 4x + 4
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