Qualification > Math

maths p1 help

(1/4) > >>

I'm a mistake - legalize abortion!:
ok can anybody help me?q.no.10 of M/J 2009


The function f is defined by f : x  ? 2x2 ? 12x + 13 for 0 ? x ? A, where A is a constant.
(i) Express f(x) in the form a(x + b)2 + c, where a, b and c are constants.
(ii) State the value of A for which the graph of y = f(x) has a line of symmetry.
(iii) When A has this value, find the range of f.
The function g is defined by g : x  ? 2x2 ? 12x + 13 for x ? 4.
(iv) Explain why g has an inverse.
(v) Obtain an expression, in terms of x, for g?1(x).

thanks in advance

Freaked12:
Sorry internet is slow right now..Paper is being downloaded.

I'm a mistake - legalize abortion!:
hello anybody there who can help?? i would be thankful :D

nid404:

--- Quote from: lord kratos on May 11, 2010, 09:07:15 pm ---ok can anybody help me?q.no.10 of M/J 2009


The function f is defined by f : x  ? 2x2 ? 12x + 13 for 0 ? x ? A, where A is a constant.
(i) Express f(x) in the form a(x + b)2 + c, where a, b and c are constants.
(ii) State the value of A for which the graph of y = f(x) has a line of symmetry.
(iii) When A has this value, find the range of f.
The function g is defined by g : x  ? 2x2 ? 12x + 13 for x ? 4.
(iv) Explain why g has an inverse.
(v) Obtain an expression, in terms of x, for g?1(x).

thanks in advance


--- End quote ---

Nid to your rescue  :)
I hope im not late

i) completing the square method 2(x-3)2-5
ii) the line of symmetry is given by -b/2a   or you can simply derivate and equate to 0
using the first method
-(-12)/ 2X2= 3
x=3 (line of symmetry passes through x=3)

second method
dy/dx= 4x-12
line of symmetry will pass through the maxima or minima as it's a quadratic
4x-12=0
x=3

u can use any method

iii) Just substitute 3 in the eqn
u get y= -5
now to decide whether this is max or min
sub 3 in d2y/dx2 = 4x
4X3=12 >0  hence minima
that mean all values of y will be greater than -5
y>=-5 is the range

iv) g has an inverse because it is a 1-1 function. It has a given set of domain.

v) y=2x2-12x-13
  We wrote this is the form (a-b)2+c
    2(x-3)2-5
y=2(x-3)2-5

make x the subject

y+5=2(x-3)2
y+5
----= (x-3)2
 2


in terms of x, so u swap the y with x

g-1(x)=

I'm a mistake - legalize abortion!:
"nid to the rescue." lol(superman)
thank u so much miss "nidman"
I hope u r not mad at me anymore

Navigation

[0] Message Index

[#] Next page