SOLUTION: Just chasing some addvice on the following. Thanks f(x)=log3(2x) and g(x)=2x^2 find fog(x)

Question 1092950: Just chasing some addvice on the following. Thanks
f(x)=log3(2x) and g(x)=2x^2 find fog(x)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
f(x) = log3(2x)

g(x) = 2x^2

fog(x) means f(x(x)).

f(g(x)) should be equal to log3(2*2x^2) = log3(4x^2)

you replace the argument of x in f(x) with g(x) = 2x^2.

that gets you f(g(x)) = log3(4x^2)

pick a random value for x.

i chose 7.

you get g(x) = 2x^2 = 2*49 = 98.

f(g(x)) = log3(4x^2) = log3(4*49) = log3(196)

if the formula is correct, then f(g(x)) should be equal to log3(196)

g(x) = 2x^2 = 2*49 = 98

f(x) = log3(2x)

f(g(x)) = log3(2*g(x)) = log3(2*98) = log3(196).

f(g(x)) is the same whether you use the formula method or you find g(x) first and then replace x with that value.

your solution is f(g(x)) = log3(2 * 2x^2) = log3(4x^2)

i'll do it one more time with another value for x so you can see the progression.

let x = 32

f(g(x)) = log3(4x^2) = log3(4*32^2) = log3(4*1024) = log3(4096)

g(x) = 2x^2 = 2*32^2 = 2*1024 = 2048

f(g(x)) = log3(2*g(x)) = log3(2*2048) = log3(4096)

they're the same.

you are replacing the argument of x in f(x) with g(x)).

f(x) = log3(2x)

the argument is x

g(x) = 2x^2

you replace the argument of x in f(x) with g(x).

g(x) is equal to 2x^2

you therefore replace the argument of x in f(x) with 2x^2.

f(x) = log3(2x) becomes f(g(x)) = log3(2 * 2x^2) which becomes log3(4x^2)
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