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) = (x-1)/2

so, solve x^2+3 = 12(x-1)/2

x^2+3 = 6x-6

x^2 - 6x + 9 = 0

(x-3)^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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