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Functions!!

f(x)=3(2^-x)-1, XER, x greater than or equal to 0

g(x)=log2x XER, x greater than or equal to 1.

Find fg(x), giving your answer in its simplest form.
Reply 1
Avatar for Esquire
Esquire
1
fg(x)=(3/x) -1
Reply 2
Avatar for yazan_l
yazan_l
5
f(x)=3(2^-x)-1, XER, x greater than or equal to 0

g(x)=log2x XER, x greater than or equal to 1.

Find fg(x), giving your answer in its simplest form.


fg(x) = f(g(x)) = f(log2x) = 3(2-log2x)-1

alogax = x
so fg(x) = 3(1/x) - 1
Reply 3
Avatar for BovineBeast
BovineBeast
Lawbutwhere?
f(x)=3(2^-x)-1, XER, x greater than or equal to 0

g(x)=log2x XER, x greater than or equal to 1.

Find fg(x), giving your answer in its simplest form.


fg(x)=f(g(x))
=3(2^-log2(x))-1

Since a^loga(x) = x, and -log(x)=1/x, 2^-log2(x)=1/x

so, fg(x)=(3/x)-1
Reply 4
Avatar for MarcosJr
MarcosJr
1
great, I tried it but didn´t remember that Since a^loga(x) = x

=/
Reply 5
Avatar for Dez
Dez
20
Just try and remember the definition of a logarithm. If you have logax, what it means is "the power to which a must be raised to produce x". So if you raise a to "the power to which a must be raised to produce x", you get x :wink:

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