Question

For f(x)=log2x and g(x)=4^x, find

a) g(f(2))
b) f(g^(-1)(64))

Answer 1

first find the g( f(x) ) by plugging in what the f(x) is equal to, INTO the g(x), INSTEAD of x.

Answer 2

So \[\log _{2}4=2\]?

Answer 3

f( g(x) ) = 4 ^ ( log_2 x)

like this

Answer 4

then plug in 2 for x/

Answer 5

I mean this is g( f(x) )

g of f, not f of g... sorry.

Answer 6

the right side of what I wrote is correct.

Answer 7

not to butt in but since is this is going to be a number, you can compute the number
\[f(2)=\log_2(2)\] (which should be more or less obvious) and then compute \(g\) of the result

Answer 8

\(\Large\color{black}{\color{red}{f(x)=\log_2x} }\)
\(\Large\color{black}{\color{blue}{g(x)=4^x} }\)

\(\Large\color{black}{\color{blue}{g(\color{red}{f(x)})=4^{\color{red}{\log_2x}}} }\)

Answer 9

\(\Large\color{black}{\color{blue}{g(\color{red}{f(x)})=4^{\color{red}{\log_2x}}} }\)

\(\Large\color{black}{\color{blue}{g(\color{red}{f(\color{darkgoldenrod}{2})})=4^{\color{red}{\log_2(\color{darkgoldenrod}{2})}}} }\)

Answer 10

then take it from there..

Answer 11

Ohhh okay, I get it now, I was forming the equation completely wrong, I don't know why I was doing it the way I was but thank you! It is much appreciated.

Answer 12

anytime:)