MATHS

posted by .

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

  • MATHS -

    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

  • MATHS -

    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

  • MATHS -

    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

  • MATHS -

    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

First Name
School Subject
Your Answer

Similar Questions

  1. 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 …
  2. coefficient

    test using the lead coefficient to find out if y arrow oo, or y arrow-oo as x arrow -oo y=-5x^3+4x^2+6x-7 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?
  3. 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 …
  4. 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?
  5. 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?
  6. 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!!!!
  7. 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 …
  8. 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 …
  9. 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 …
  10. Physics

    An arrow is fired horizontally with a speed of 30ms-1 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 …

More Similar Questions