Posted by CHLOE on .
Critical help please. Level 3 maths algebraic methods is really hard.
Two functions f and g are defined by
f:x (arrow) x^2 + 3
g:x (arrow) 2x+1
a) the function fg
b) solve the equation f(x)=12g^-1(x)
I need to show my working out, please help someone
by fg I assume you mean f*g
f*g = (x^2+3)*(2x+1) = 2x^3 + x^2 + 6x + 3
g=2x+1, so g^-1 = (x-1)/2
so, if f = 12 g^-1,
x^2+3 = 12 * (x-1)/2
x^2+3 = 6x-6
x^2 - 6x + 9 = 0
(x-3)^2 = 0
x = 3
Thank you steve
It says i need to find f(g), i got a different result for some reason help please!
And also in the second part, how did you get g^-1 = (x-1)/2
Thank you steve x
That's because fg is ambiguous. I did f(x) * g(x).
f◦g = f(g) = g^2+3 = (2x+1)^2+3
= 4x^2 + 4x + 4
to get g^-1, just solve for x
g = 2x+1
g-1 = 2x
x = (g-1)/2
then switch variables, and g^-1 = (x-1)/2
Is there any reason why f(g)=g^2+3
why do we replace the x with g?
Sorry steve im trying my hardest to understand this