# Thread: VCE Maths questions help

1. ## Re: VCE Maths questions help Originally Posted by boredsatan Bump!
Bump!  Reply With Quote

2. ## Re: VCE Maths questions help

f(x) = sqrt(x+1), and has a restricted domain of [0, infinity)
g(x) = x^2+4x+3, and has a restricted domain of (-infinity, -3]
How would i find the range of f(g(x)) without a calculator?  Reply With Quote

3. ## Re: VCE Maths questions help Originally Posted by boredsatan f(x) = sqrt(x+1), and has a restricted domain of [0, infinity)
g(x) = x^2+4x+3, and has a restricted domain of (-infinity, -3]
How would i find the range of f(g(x)) without a calculator?
bump  Reply With Quote

4. ## Re: VCE Maths questions help Originally Posted by boredsatan bump
Have you found and simplified f(g(x))? Once you do this, you should be able to do the question.  Reply With Quote

5. ## Re: VCE Maths questions help Originally Posted by InteGrand Have you found and simplified f(g(x))? Once you do this, you should be able to do the question.
f(g(x)) = sqrt(x^2+4x+4), so would I use the domain of g(x) as the domain of f(g(x))?  Reply With Quote

6. ## Re: VCE Maths questions help

Is the square root of 4 just 2 or both 2 and -2?  Reply With Quote

7. ## Re: VCE Maths questions help

Bump  Reply With Quote

8. ## Re: VCE Maths questions help Originally Posted by boredsatan Bump
Bump  Reply With Quote

9. ## Re: VCE Maths questions help

Square rooting is usually principal root, so omly +ve case  Reply With Quote

10. ## Re: VCE Maths questions help

Is this always the case that you only take the +ve?  Reply With Quote

11. ## Re: VCE Maths questions help

bump  Reply With Quote

12. ## Re: VCE Maths questions help Originally Posted by boredsatan bump
can someone please answer my questions?  Reply With Quote

13. ## Re: VCE Maths questions help

bump  Reply With Quote

14. ## Re: VCE Maths questions help Originally Posted by boredsatan bump
bump please  Reply With Quote

15. ## Re: VCE Maths questions help Originally Posted by boredsatan bump please
bump  Reply With Quote

16. ## Re: VCE Maths questions help

2sin(2x-pi/6) = 1 for a domain of -pi<x<pi
we multiply the domain values of 2, so it becomes -2pi<2x<2pi
but then do we subtract the domain values by -pi/6
or since 2sin(2x-pi/6) = 2sin(2(x-pi/12)), do we subtract the domain values by -pi/12?
Thanks  Reply With Quote

17. ## Re: VCE Maths questions help Originally Posted by boredsatan 2sin(2x-pi/6) = 1 for a domain of -pi<x<pi
we multiply the domain values of 2, so it becomes -2pi<2x<2pi
but then do we subtract the domain values by -pi/6
or since 2sin(2x-pi/6) = 2sin(2(x-pi/12)), do we subtract the domain values by -pi/12?
Thanks
bump  Reply With Quote

18. ## Re: VCE Maths questions help Originally Posted by boredsatan Is this always the case that you only take the +ve?
It depends on the notation.

is a function that denotes taking the principal square root, which is always the positive one, for real .

However, for always has two solutions.  Reply With Quote

19. ## Re: VCE Maths questions help

if we had to find the derivative of sqrt(x^2+3), and evaluate it when x = 1, we get 1/(sqrt(4)), which so in this case, would it be 1/2 and 1/-2?
or just 1/2?  Reply With Quote

20. ## Re: VCE Maths questions help Originally Posted by boredsatan if we had to find the derivative of sqrt(x^2+3), and evaluate it when x = 1, we get 1/(sqrt(4)), which so in this case, would it be 1/2 and 1/-2?
or just 1/2?
Just 1/2.  Reply With Quote

21. ## Re: VCE Maths questions help Originally Posted by InteGrand Just 1/2.
So in what cass is the square root both the +ve and -ve and in what cases is it only the +ve?

Also can someone please help me with the below questions?
2sin(2x-pi/6) = 1 for a domain of -pi<x<pi
we multiply the domain values of 2, so it becomes -2pi<2x<2pi
but then do we subtract the domain values by -pi/6
or since 2sin(2x-pi/6) = 2sin(2(x-pi/12)), do we subtract the domain values by -pi/12?
Thanks

f(x) = sqrt(x+1), and has a restricted domain of [0, infinity)
g(x) = x^2+4x+3, and has a restricted domain of (-infinity, -3]
How would i find the range of f(g(x)) without a calculator?
f(g(x)) = sqrt(x^2+4x+4), so would I use the domain of g(x) as the domain of f(g(x))?  Reply With Quote

22. ## Re: VCE Maths questions help Originally Posted by boredsatan So in what cass is the square root both the +ve and -ve and in what cases is it only the +ve?

Also can someone please help me with the below questions?
2sin(2x-pi/6) = 1 for a domain of -pi<x<pi
we multiply the domain values of 2, so it becomes -2pi<2x<2pi
but then do we subtract the domain values by -pi/6
or since 2sin(2x-pi/6) = 2sin(2(x-pi/12)), do we subtract the domain values by -pi/12?
Thanks

f(x) = sqrt(x+1), and has a restricted domain of [0, infinity)
g(x) = x^2+4x+3, and has a restricted domain of (-infinity, -3]
How would i find the range of f(g(x)) without a calculator?
f(g(x)) = sqrt(x^2+4x+4), so would I use the domain of g(x) as the domain of f(g(x))?  Reply With Quote

23. ## Re: VCE Maths questions help Originally Posted by boredsatan Also can someone please help me with the below questions?
2sin(2x-pi/6) = 1 for a domain of -pi<x<pi
we multiply the domain values of 2, so it becomes -2pi<2x<2pi
but then do we subtract the domain values by -pi/6
or since 2sin(2x-pi/6) = 2sin(2(x-pi/12)), do we subtract the domain values by -pi/12?
Thanks
You don't need to do anything, because the domain is already given to us.  Reply With Quote

24. ## Re: VCE Maths questions help Originally Posted by boredsatan So in what cass is the square root both the +ve and -ve and in what cases is it only the +ve?

Also can someone please help me with the below questions?
2sin(2x-pi/6) = 1 for a domain of -pi<x<pi
we multiply the domain values of 2, so it becomes -2pi<2x<2pi
but then do we subtract the domain values by -pi/6
or since 2sin(2x-pi/6) = 2sin(2(x-pi/12)), do we subtract the domain values by -pi/12?
Thanks

f(x) = sqrt(x+1), and has a restricted domain of [0, infinity)
g(x) = x^2+4x+3, and has a restricted domain of (-infinity, -3]
How would i find the range of f(g(x)) without a calculator?
f(g(x)) = sqrt(x^2+4x+4), so would I use the domain of g(x) as the domain of f(g(x))?  Reply With Quote

25. ## Re: VCE Maths questions help Originally Posted by InteGrand What do you mean? Would the domain of f(g(x)) just be the domain of g(x), which in this case is restricted to (-infinity,-3]?  Reply With Quote

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