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Mathematics: Post your doubts here!

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10 The function f is defined by f : x → 2x
2 − 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 → 2x
2 − 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). [3]
 
ZaqZainab

ZaqZainab

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usama321 said:
Actually it would be done this way. I was also confused about it

f (x) = hg(x)
(x-2)^2 + 3
Now, since hg is a composite function, the value of g, which is x-2, would have to be put into the value of h in such a way that it becomes, (x-2)^2 + 3.

Thus h would be x^2 + 3. You can put in the value of g now and you will get f(x)
Click to expand...
how did you end up with x^2 +3
 
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XPFMember said:
Re: Maths help available here!!! Stuck somewhere?? Ask here!

Assalamoalaikum!! :)

UPDATE: Link to Sequences Help by destined007 added!
Click to expand...
10 The function f is defined by f : x → 2x
2 − 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 → 2x
2 − 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). [3]
help please
 
usama321

usama321

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ZaqZainab said:
View attachment 39573
Click to expand...
Its a composite function hg(x)

Since g(x) = x-2 and we have to make it equal to (x-2)^2 + 3,
Now in composite functions, we take the value of one function, and replace the variable x in the other function with that value.

Now for hg be equal to (x-2)^2 + 3, we need to do g^2 + 3. As in composite functions we replace the x with another function, we will put that x back in. Thus it would become x^2 + 3. Now put instead of x the value of g(x), and it becomes
(x-2)^2 + 3
 
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usama321 said:
Its a composite function hg(x)

Since g(x) = x-2 and we have to make it equal to (x-2)^2 + 3,
Now in composite functions, we take the value of one function, and replace the variable x in the other function with that value.

Now for hg be equal to (x-2)^2 + 3, we need to do g^2 + 3. As in composite functions we replace the x with another function, we will put that x back in. Thus it would become x^2 + 3. Now put instead of x the value of g(x), and it becomes
(x-2)^2 + 3
Click to expand...
Was it that easy ?
 
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usama321 said:
Kindly tell me what you define as easy. If you take for granted that a one mark question is easy, than of course it was easy. If you define a question that requires more than average logic, and frustrates you as easy, than it was easy once again.

p.s i saw someone else's solution. wasn't able to do it myself
Click to expand...
Oh, but I get to know your solution well, it was easy, I too got the same way! But I thought it might be wrong. SO I DIDNT POST IT! :p
 
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