Question

Critical help please. Level 3 maths algebraic methods is really hard.

Q)
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)

I need to show my working out, please help someone

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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