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

1. anonymous

2. anonymous

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

first step is to narrow it down to D and E, since those are the only ones that make remote sense

4. Vocaloid

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

if we let a = 1 and b = 2, see whether f(a) or f(b) is bigger.

6. anonymous

(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

@Vocaloid which would be the a or the c in this?

8. Vocaloid

?

9. Vocaloid

just calculate f(a) when a = 1

10. anonymous

is the answer E, because its a whole fraccion?

11. anonymous

and how you know a its 1 ?

12. Vocaloid

I just picked a value for a

13. Vocaloid

the question just says a < b so I just picked a = 1 and b = 2 as test values

14. Vocaloid

you can pick any two numbers for a and b as long as a < b

15. Vocaloid

the point of me picking a = 1 and b = 2, was just to see whether f(a) or f(b) was bigger

16. anonymous

b is the exponent right?

17. Vocaloid

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

$\left( \frac{ 1 }{ 3 } \right)^2=\frac{ 1 }{ 9 },$ $\left( \frac{ 1 }{ 3 } \right)^3=\frac{ 1 }{ 27 }$ 2<3 $\frac{ 1 }{ 9 } ?\frac{ 1 }{ 27 }$

19. anonymous

yeah its true @surjithayer 1/9 is bigger than 1/27