MATHS
posted by CHLOE
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

Steve
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 = (x1)/2
so, if f = 12 g^1,
x^2+3 = 12 * (x1)/2
x^2+3 = 6x6
x^2  6x + 9 = 0
(x3)^2 = 0
x = 3 
CHLOE
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 = (x1)/2
Thank you steve x 
Steve
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
g1 = 2x
x = (g1)/2
then switch variables, and g^1 = (x1)/2 
CHLOE
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
Respond to this Question
Similar Questions

Calculus
We're learning about different kinds of functions and I don't really understand the difference between rational and algebraic functions. I know that rational functions are functions that are a ratio of two polynomials, and algebraic … 
coefficient
test using the lead coefficient to find out if y arrow oo, or y arrowoo as x arrow oo y=5x^3+4x^2+6x7 n is odd 5x^3 an<0 5x^3 y arrow oo as x arrow oo Is this right or do I need to go back and try again? 
physics!
A girl shoots an arrow from the top of a cliff. The arrow is initially at a point 20 meters above the level field below. The arrow is shot at an angle of 30 degrees above the horizontal with a speed of 39.2m/s. How far out from the … 
Physics
Three arrows are shot at different angles. A red arrow is shot at 30degrees, a blue arrow is shot at 45degrees, and a yellow arrow is shot at 60degrees. A) Which arrow goes the farthest? 
Math  Derivative of a polynomial function
A flaming arrow is shot into the air to mark the beginning of the a festival. Its height, h, in meters after t seconds can be modelled by the function h(t)=4.9t^2+24.5t+2 How fast is the arrow traveling when it hits the ground? 
Maths
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!!!! 
Complex Algaebra, Plz Help!!
Good evening to all around the world. Need help with this question, however i must show my answers supported by the working out. Please help. This question is difficult, the one who solves it for me is my hero!!!! Q11) Two functions … 
algebra
An archer releases an arrow from a shoulder height of 1.39 m. When the arrow hits the target 18 m away, it hits point A. When the target is removed, the arrow lands 45 m away. Find the maximum height of the arrow along its parabolic … 
physics vectors
Consider the two vectors A with arrow = 3 i − j and B with arrow = − i − 6 j. Calculate the directions of A with arrow + B with arrow and A with arrow − B with arrow. A with arrow + B with arrow ° (counterclockwise … 
Physics
An arrow is fired horizontally with a speed of 30ms1 from a height of 2m above the ground level. Model the arrow as a particle which does not experience air resistance. a)show that the time taken for the arrow to hit the ground is …