Author Topic: P1,functions  (Read 1036 times)

Offline thecandydoll

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P1,functions
« on: May 05, 2010, 08:02:37 am »
10 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. [3]
(ii) State the value of A for which the graph of y = f(x) has a line of symmetry. [1]
(iii) When A has this value, find the range of f. [2]
The function g is defined by g : x  ? 2x2 ? 12x + 13 for x ? 4.
(iv) Explain why g has an inverse. [1]
(v) Obtain an expression, in terms of x, for g?1(x).

Could you also find the range and domain for g?
With explanation.I really don't get it thanks a lot
X

~ A.F ~

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Re: P1,functions
« Reply #1 on: May 05, 2010, 08:04:17 am »
what's the "?" in your righting

Offline astarmathsandphysics

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Re: P1,functions
« Reply #2 on: May 05, 2010, 08:10:11 am »
There are notes for this on my website. Unfortunately i have been called into central london again.

Offline dlehddud

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Re: P1,functions
« Reply #3 on: May 05, 2010, 08:26:43 am »
I don't get what you mean by the '?'  ??? ??? ???
I swear exams are going to be the end of me someday

Offline thecandydoll

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Re: P1,functions
« Reply #4 on: May 05, 2010, 11:22:29 am »
it is supposed to be inverse.
typo.
sorryy.
can you help me?

Offline simba

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Re: P1,functions
« Reply #5 on: May 07, 2010, 10:17:34 am »
excuse me guyz, but I want to know how to get the range when he asks me in the question???

plz reply URGENT

Offline astarmathsandphysics

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Re: P1,functions
« Reply #6 on: May 07, 2010, 09:29:34 pm »
10 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. [3]
(ii) State the value of A for which the graph of y = f(x) has a line of symmetry. [1]
(iii) When A has this value, find the range of f. [2]
The function g is defined by g : x  ? 2x2 ? 12x + 13 for x ? 4.
(iv) Explain why g has an inverse. [1]
(v) Obtain an expression, in terms of x, for g?1(x).

I will assumef(x)=x^2 +12x+13
f(x)=(x+12/2)^2 +13-(12/2)^2=(x+6)^2-23
line of symmetry at x=-6
range is (-23, \infinity) since (x+6)^2 >0

g has an inversrse because there is only one g(x) for every value of x
g^{-1} =sqrt{x+23} -6

see http://www.astarmathsandphysics.com/a_level_maths_notes/C3/a_level_maths_notes_c3_inverting_functions.html