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anonymous

  • one year ago

please help if f(x)=(1/3)^x and a<b, which of the following must be true?

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  1. anonymous
    • one year ago
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    ..are there any answer choices?

  2. anonymous
    • one year ago
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    Yes @jacquelyn1237 A.f(a)+ f(b)=3 B f(a) + 1/3=f(b) C f(a)= f(b) D. f (a) < f(b) E. f (a) >f(b)

  3. Vocaloid
    • one year ago
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    first step is to narrow it down to D and E, since those are the only ones that make remote sense

  4. Vocaloid
    • one year ago
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    an easy way to distinguish whether f(a) or f(b) is bigger is just to pick two numbers for a and b and see which one ends up bigger

  5. Vocaloid
    • one year ago
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    if we let a = 1 and b = 2, see whether f(a) or f(b) is bigger.

  6. anonymous
    • one year ago
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    (you can rule out choices A and B because the questions asks which one "must" be true" and those only work for certain numbers)

  7. anonymous
    • one year ago
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    @Vocaloid which would be the a or the c in this?

  8. Vocaloid
    • one year ago
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    ?

  9. Vocaloid
    • one year ago
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    just calculate f(a) when a = 1

  10. anonymous
    • one year ago
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    is the answer E, because its a whole fraccion?

  11. anonymous
    • one year ago
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    and how you know a its 1 ?

  12. Vocaloid
    • one year ago
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    I just picked a value for a

  13. Vocaloid
    • one year ago
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    the question just says a < b so I just picked a = 1 and b = 2 as test values

  14. Vocaloid
    • one year ago
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    you can pick any two numbers for a and b as long as a < b

  15. Vocaloid
    • one year ago
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    the point of me picking a = 1 and b = 2, was just to see whether f(a) or f(b) was bigger

  16. anonymous
    • one year ago
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    b is the exponent right?

  17. Vocaloid
    • one year ago
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    f(x) = (1/3)^x f(a) = (1/3)^a f(b) = (1/3)^b find f(a) and f(b) if a = 1 and b = 2

  18. anonymous
    • one year ago
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    \[\left( \frac{ 1 }{ 3 } \right)^2=\frac{ 1 }{ 9 },\] \[\left( \frac{ 1 }{ 3 } \right)^3=\frac{ 1 }{ 27 }\] 2<3 \[\frac{ 1 }{ 9 } ?\frac{ 1 }{ 27 }\]

  19. anonymous
    • one year ago
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    yeah its true @surjithayer 1/9 is bigger than 1/27

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