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cwrw238

  • 3 years ago

I'm helping my nephew with a function question and i'm stuck on one part - I should know this really. f(x) = x^2 - 19, domain = (-INF, 0) g(x) = 1 -(1/2) x, domain = (6, INF). Find range of f and g which i found to be (-19, INF) and (-INF, -2). Find fg - which I got to be (1 - (1/2)x)^2 - 19. Write down the domain and range of fg. - i'm a bit confused about this part.

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  1. cwrw238
    • 3 years ago
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    I've done this stuff before but cant remember this bit.

  2. hsmt
    • 3 years ago
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    hi. i think i can help. consider the intersection of the two domains

  3. hsmt
    • 3 years ago
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    what is the intersection of the two domains?

  4. cwrw238
    • 3 years ago
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    well they dont intersect - which makes me think that the domain is that of g (6, INF)

  5. hsmt
    • 3 years ago
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    the domain is the null set. and thus, it has not range either

  6. hsmt
    • 3 years ago
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    it has no* range either

  7. hsmt
    • 3 years ago
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    does that make sense to you?

  8. cwrw238
    • 3 years ago
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    hmm - not sure to be honest - i'm not saying you're wrong - but i'll have to go back to the books thanx for your comments

  9. hsmt
    • 3 years ago
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    sure, the product, quotient and sums of two functions need to have intersecting domains

  10. hsmt
    • 3 years ago
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    otherwise the function is not defined. I hope that helps. Take care.

  11. cwrw238
    • 3 years ago
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    ty

  12. cwrw238
    • 3 years ago
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    I've checked this out - because the domain of 'inner' function is (6.infinity) the composite function must have same domain - they intersect at that range of values hers a rough (lol) drawing

  13. cwrw238
    • 3 years ago
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    |dw:1348438040718:dw|

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