Which functions are correct? f(x) = 24x g(x) = 2x Choose exactly two answers that are correct.

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Which functions are correct? f(x) = 24x g(x) = 2x Choose exactly two answers that are correct.

Mathematics
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\[\large\rm f(x)=2^{4x},\qquad\qquad g(x)=2^x\]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.
So what do you think? :o

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Other answers:

sounds difficult
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?
the first one i guess
Good. And our division rule tells us to `subtract` the exponents.\[\large\rm \frac{f}{g}=\frac{2^{4x}}{2^x}=2^{4x-x}\]
x-x = 0 ?
It's 4x-x. Not x-x.
4apples - an apple
but why is it asking for 2 right answers?
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.
what you think about A snd C?
agree
yay good job
they correct?

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