Question

Which functions are correct?

f(x) = 24x g(x) = 2x

Choose exactly two answers that are correct.

Answer 1

\[\large\rm f(x)=2^{4x},\qquad\qquad g(x)=2^x\]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.

Answer 2

So what do you think? :o

Answer 3

sounds difficult

Answer 4

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?

Answer 5

the first one
i guess

Answer 6

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

Answer 7

x-x = 0
?

Answer 8

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

Answer 9

4apples - an apple

Answer 10

but why is it asking for 2 right answers?

Answer 11

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.

Answer 12

what you think about A snd C?

Answer 13

agree

Answer 14

yay good job

Answer 15

they correct?