Function Question(CAn i get full mark in SPM)

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[Yap Yee Soon]

Can i get full mark if using this solution:
1) Given that f(x) = 2x - 1 and fg(x) = 3x², find g(x)
Answer:
let
y = 2x - 1
x = ( y + 1 )/2
f^-1(x)= ( x + 1 )/2
g(x) = f^-1[fg(x)]
      = f^-1(3x²)
      = ((3x²) + 1 ) / 2

2) Given that g(x) = 2x - 1 and fg(x) = 3x², find f(x)
Answer:
let
y = 2x - 1
x = ( y + 1 )/2
g^-1(x)= ( x + 1 )/2
f(x) = fg[g^-1(x)]
      =fg(( x + 1 )/2)
      = 3[( x + 1 )/2]²
      = 3( x + 1 )²/4

[Yap Yee Soon]

Any one can answer my question? i mean in SPM marking, did these 2 solution get full marks?

[Foo Tze Yaw]

I don't know from which reference book you get these questions from. And I don't know how many marks are allocated for each of your question. But I think such questions usually come out in paper 1. From what I know in paper 1, you get full marks if your final answer is correct, regardless of whatever steps you have written.

I'm not a guru cemerlang, nor have I been an examiner of SPM 3472 before. But I can share with you how I'll mark such solutions. The marking scheme I'll make is as follows:

<Question>	<Key Solution / Step>	<SubMark>	<FullMark>
1	(3x2 + 1) / 2	2	2
	u = (x + 1) / 2  or  equivalent	B1
2	(3x2 + 6x + 3) / 4  or  [3(x + 1)2] / 4  or  3/4 (x + 1)2	3	3
	f(u) = 3[(u + 1) / 2]2  or  equivalent	B2
	f(2x - 1) = 3x2  or  x = (u + 1) / 2	B1

Based on the marking scheme, i'll give full marks (3 marks) for your question 2, but only 1 mark (B1) for your question 1. This is because i assume you are still writing inner bracket for 3x² term, which is unnecessary, and strictly speaking, not accepted as the simplest form. So the B1 mark i give for your question 1 is because you did write the framework for the inverse function, which is x = (y + 1) / 2.

[Yap Yee Soon]

Thank ypu Mr Foo, Any other teachers who are experience in marking can give some comment? if these question come out in paper 2, can the students get full marks?

[Chong Lee Khim]

Dear sir,
      I can answer your question that there is no mark to be deducted according to your working steps, if the question comes out in paper 2.



Can i get full mark if using this solution:
1) Given that f(x) = 2x - 1 and fg(x) = 3x2, find g(x)
Answer:
let
y = 2x - 1
x = ( y + 1 )/2          1 mark
f-1(x)= ( x + 1 )/2      alternative method:  fg(x) = 2g(x) - 1 = 3x²         
g(x) = f-1[fg(x)]                 2g(x) = 3x² +1     
      = f-1(3x2)                   g(x) = (3x² + 1)/2   
      = ((3x2) + 1 ) / 2  1 mark

2) Given that g(x) = 2x - 1 and fg(x) = 3x2, find f(x)
Answer:
let
y = 2x - 1
x = ( y + 1 )/2     1 mark
g-1(x)= ( x + 1 )/2            fg(x) = f(y)
f(x) = fg[g-1(x)]                    = 3[(y + 1)/2]²
      =fg(( x + 1 )/2)
      = 3[( x + 1 )/2]2 ---1 mark   so, f(x) = 3(x + 1)²/4
      = 3( x + 1 )2/4  ---1 mark

[Yap Yee Soon]

thank you Ms Chong,
Any other teacher can give some comment esp the method of using in question 1 compare the method using on text book?

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