Another HSC Q

A

AlonzoN

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let f(x) = √(x+1) for x>=0

i. state the range of f(x), and I said that y >= 1

but for ii. it's asking me to let g(x) = x^2 +4x +3, where x<= c and c<= 0. Find the largest possible value of c such that the range of g(X) is a subset of the domain of f(x).
 
I don't know what HSC means ...

Do you know what "subset" means?

If you sketch g(x) and pick some non-positive value of c, can you see what the range of that restricted function will be?

For example, if we take c = 0, what is that range? Is it a subset of the range of f? How about if c = -4?
 
Dr.Peterson said:
I don't know what HSC means ...

Do you know what "subset" means?

If you sketch g(x) and pick some non-positive value of c, can you see what the range of that restricted function will be?

For example, if we take c = 0, what is that range? Is it a subset of the range of f? How about if c = -4?
Click to expand...
So what do I do? Plug -4 as c, then make x = -4?
 
Dr P, HSC stands for Higher School Certificate. The HSC exam is a statewide exam for final year high school students in the state of New South Wales in Australia.
 
AlonzoN said:
let f(x) = √(x+1) for x>=0

i. state the range of f(x), and I said that y >= 1

but for ii. it's asking me to let g(x) = x^2 +4x +3, where x<= c and c<= 0. Find the largest possible value of c such that the range of g(X) is a subset of the domain of f(x).
Click to expand...
Can you check the question? Is the last bit of ii. "the domain of f(x)" or is it supposed to be "the range of f(x)"?
 
oh np, so it's asking to find the Largest possible value of c such that the range of g(x) is a subset of the domain of f(x)
 
I'm confused. Where you have written domain, is it meant to be range? Check the question on the exam.
 
let f(x) = √(x+1)vfor x>=0

i. state the range of f(x)

ii. let g(x) = x^2 + 4x +3, where x<= c and c <= 0

find the largest possible value of c such that the range of g(x) is a subset of the domain of f(x)

at first, I though it might be 3.
 
Ok, so what is the domain of f(x)?
And what is the range of g(x)=x^2+4x+3 (forget the c bit for the moment)
 
Good. So at the moment, the range of g(x) is NOT a subset of the domain of f(x), because it is a bigger set of numbers, ie the range of g includes numbers between -1 and 0, but the domain of f doesn't. Get that?
 
Yes that's right. So, we have to restrict the domain of g(x), so that the range of g(x) doesn't include any numbers that are < 0. Get that?
 
We have to restrict the domain of g , according to the question, by x<=c where c<= 0.
Have you sketched the graph of g?
 
Good so at the moment, without any restrictions on what x can be, the range of g is from -1 and above.
We don't want that. We don't want to include the negative values of y in the range, so we need to rub them out.
Can you now see what c must be? Remember we want the domain to be x<=c, so that the range doesn't include the bit under the x-axis.
 
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