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Thread: VCE Maths questions help

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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    Bump!
    Bump!
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    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?
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    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
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    bump
    Have you found and simplified f(g(x))? Once you do this, you should be able to do the question.

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    Re: VCE Maths questions help

    Quote Originally Posted by InteGrand View Post
    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))?
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    Re: VCE Maths questions help

    Is the square root of 4 just 2 or both 2 and -2?
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    Re: VCE Maths questions help

    Bump
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    Bump
    Bump
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    Re: VCE Maths questions help

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

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    Re: VCE Maths questions help

    Is this always the case that you only take the +ve?
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    Re: VCE Maths questions help

    bump
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    bump
    can someone please answer my questions?
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    Re: VCE Maths questions help

    bump
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    bump
    bump please
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    bump please
    bump
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    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
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    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
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    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.

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    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?
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    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.

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    Re: VCE Maths questions help

    Quote Originally Posted by InteGrand View Post
    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))?
    year 11 2017
    year 12 2018
    year boredsatan 2019
    year LOL 2020-infinity

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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    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))?

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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    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.

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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    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))?

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    Re: VCE Maths questions help

    Quote Originally Posted by InteGrand View Post
    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]?
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