Help ASAP thank you Consider the composite function g(f(x)) = x16.
If f(x) = 3x2, what is g(x)?
O g(x) = /2x
O g(x)=x+3
O g(x) = 5x
O g(x)=79- x

Choice A

g(x) = sqrt(2x)

Explanation:

"sqrt(x)" is shorthand for "square root of x"

f(x) = 3x^2 is given

g( f(x) ) = x*sqrt(6) is also given

One way to find the answer is through trial and error. This would only apply of course if we're given a list of multiple choice answers.

Let's start with choice A

g(x) = sqrt(2x)

g( f(x) ) = sqrt(2 * f(x) ) replace every x with f(x)

g( f(x) ) = sqrt(2 * 3x^2 ) plug in f(x) = 3x^2

g( f(x) ) = sqrt(6x^2 )

g( f(x) ) = sqrt(x^2 * 6)

g( f(x) ) = sqrt(x^2)*sqrt(6)

g( f(x) ) = x*sqrt(6)

We found the answer on the first try. So we don't need to check the others.

But let's try choice B to see one where it doesn't work out

g(x) = sqrt(x + 3)

g( f(x) ) = sqrt( f(x) + 3)

g( f(x) ) = sqrt(3x^2 + 3)

and we can't go any further other than maybe to factor 3x^2+3 into 3(x^2+1), but that doesn't help things much to be able to break up the root into anything useful. We can graph y = x*sqrt(6) and y = sqrt(3x^2 + 3) to see they are two different curves, so there's no way they are equivalent expressions.

Answer is A g(x) = sqrt(2x)

Step-by-step explanation:

Answer is A if you use edgenuity, answers do not mix.  

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