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Math Help - plz try this simple quest..the ans is different as i calculated.

  1. #1
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    plz try this simple quest..the ans is different as i calculated.

    find natural domain and range for each function:
    a) G(x)=(x^2-2*x+5)^(1/2)

    b)h(x)=1/(1-sin(x))

    c)H(x)=(sin(x^(1/2)))^(-2)
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  2. #2
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    Quote Originally Posted by redcherry View Post
    find natural domain and range for each function:
    a) G(x)=(x^2-2*x+5)^(1/2)

    b)h(x)=1/(1-sin(x))

    c)H(x)=(sin(x^(1/2)))^(-2)
    Your post title suggests that you have attempted to solve these and apparently got answers different to what the answers are meant to be. So please show all the details of your calculations and include your answers.
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  3. #3
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    tq for reply~

    i just use this formula to find the roots which men the values of x..
    (-b+(b^2-4*a*c))/2*a and got the ans x=1+4i and x=1-4i
    but the ans for the domain is x=real number and the range y>=2.
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  4. #4
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    Quote Originally Posted by redcherry View Post
    i just use this formula to find the roots which men the values of x..
    (-b+(b^2-4*a*c))/2*a and got the ans x=1+4i and x=1-4i
    but the ans for the domain is x=real number and the range y>=2.
    What you posted is not what I consider detailed working.

    a) Domain: Solve x^2-2x+5 \geq 0.

    b) Domain: All real numbers except those satisfying 1-sin(x) = 0.

    c) Domain: All positive real numbers except those satisfying \sin(\sqrt{x}) = 0.

    The details are left for you. I suggest you get ranges by drawing graphs. For a) note that y=(x^2-2x+5)^{1/2} \Rightarrow y^2 = x^2 - 2x + 5 and you should recognise a branch of a hyperbola.
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  5. #5
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    ok..

    for b) i got the domain x is not equal (2*n+1/2)*Pi but i didnt got the range
    for c) the domain x is not equal (n*Pi)^2 and also didnt get the range..
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  6. #6
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    Quote Originally Posted by redcherry View Post
    for b) i got the domain x is not equal (2*n+1/2)*Pi but i didnt got the range
    for c) the domain x is not equal (n*Pi)^2 and also didnt get the range..
    Draw the graphs. eg. b) Draw the graph of f(x) = -\sin (x) + 1 and then use the standard properties of reciprocal functions to draw h(x) = \frac{1}{f(x)}.
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  7. #7
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    Quote Originally Posted by mr fantastic View Post
    Draw the graphs. eg. b) Draw the graph of f(x) = -\sin (x) + 1 and then use the standard properties of reciprocal functions to draw h(x) = \frac{1}{f(x)}.
    Alternatively, to find the natural range of each function, find the domain of each inverse function...
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