## anonymous one year ago Which functions are correct? f(x) = 24x g(x) = 2x Choose exactly two answers that are correct.

1. anonymous

2. zepdrix

$\large\rm f(x)=2^{4x},\qquad\qquad g(x)=2^x$So then,$\large\rm (fg)(x)=2^{4x}\cdot 2^x$As a reminder, here is our relevant exponential rule:$\large\rm \color{orangered}{a^x\cdot a^y=a^{x+y}}$It tells us that when we multiply things that have the same base, we add the exponents.

3. zepdrix

So what do you think? :o

4. anonymous

sounds difficult

5. zepdrix

So these are your two options:$\large\rm 2^{4x}\cdot2^{x}=2^{4x+x}$$\large\rm 2^{4x}\cdot2^{x}=2^{4x\cdot x}$ Based on the rule I posted, which one seems correct?

6. anonymous

the first one i guess

7. zepdrix

Good. And our division rule tells us to subtract the exponents.$\large\rm \frac{f}{g}=\frac{2^{4x}}{2^x}=2^{4x-x}$

8. anonymous

x-x = 0 ?

9. zepdrix

It's 4x-x. Not x-x.

10. zepdrix

4apples - an apple

11. anonymous

12. zepdrix

Because we chose one correct answer for $$\large\rm (fg)(x)$$, multiplication of these functions. We also need to chose one correct answer for $$\large\rm \left(\frac{f}{g}\right)(x)$$, division of these functions.

13. anonymous

what you think about A snd C?

14. triciaal

agree

15. zepdrix

yay good job

16. anonymous

they correct?