IGCSE/GCSE/O & A Level/IB/University Student Forum

Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: thecandydoll on May 05, 2010, 08:02:37 am

Title: P1,functions
Post by: thecandydoll 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
Title: Re: P1,functions
Post by: ~ A.F ~ on May 05, 2010, 08:04:17 am: what's the "?" in your righting
Title: Re: P1,functions
Post by: astarmathsandphysics 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.
Title: Re: P1,functions
Post by: dlehddud on May 05, 2010, 08:26:43 am: I don't get what you mean by the '?' ??? ??? ???
Title: Re: P1,functions
Post by: thecandydoll on May 05, 2010, 11:22:29 am: it is supposed to be inverse.
typo.
sorryy.
can you help me?
Title: Re: P1,functions
Post by: simba 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
Title: Re: P1,functions
Post by: astarmathsandphysics 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 assume $f(x)=x^2 +12x+13$
$f(x)=(x+12/2)^2 +13-(12/2)^2=(x+6)^2-23$
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