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Math Help - Find the domain and range of the function

  1. #1
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    Find the domain and range of the function

    A isosceles triangel has the perimeter 10 cm. Signb for the base and s for the sides.
    Decide the function's domain and range. According to the key the answers should be:
    D:0<s<5
    V: 0<v<10.

    How can these answers be possible? If the base are 9 cm, then the two sides of the triangel have to be 0.5 cm each and then they will not form a triangel. Can you please explain? Thank you in advance.
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  2. #2
    Member Goku's Avatar
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    b = 10 -2s

    since b>0
    10-2s>0
    s<5
    then
    D:0<s<5
    V: 0<v<10.

    if b=9
    then s=0.5, this forms a triangle, why wouldn't it I'm confused??
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Anna55 View Post
    A isosceles triangel has the perimeter 10 cm. Signb for the base and s for the sides.
    Decide the function's domain and range. According to the key the answers should be:
    D:0<s<5
    V: 0<v<10.

    How can these answers be possible? If the base are 9 cm, then the two sides of the triangel have to be 0.5 cm each and then they will not form a triangel. Can you please explain? Thank you in advance.
    You are correct. There is a formula called the "Triangle Inequality." I won't state it, but the content is that the sum of any two sides of a triangle is greater than the third side. In your case the pertinent inequality is that the sum of the sides of the triangle has to be greater than the size of the base: 2s > b. Along with that you have b + 2s = 10. Thus, for example, b = 10 - 2s and 2s > b means that 2s > 10 - 2s.

    Can you finish from here? (You can make a similar solution for b by solving the b + 2s = 10 equation for s and sticking that into the inequality.)

    -Dan
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Goku View Post
    if b=9
    then s=0.5, this forms a triangle, why wouldn't it I'm confused??
    Have you tried to sketch this? The two sides s do not meet at a vertex.

    -Dan
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  5. #5
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    Should I continue like this:

    2s>10-2s
    4s>10
    s>2.5
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Anna55 View Post
    Should I continue like this:

    2s>10-2s
    4s>10
    s>2.5
    Yup! Now do the same for b.

    -Dan
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