Question

I need help with this question

Answer 1

`6\sqrt6`

Explanation:

We can solve for
`f(g(x))` for a given x-value (4) by:

1. plugging the x-value into g(x) and solving for its output
2. plugging the output from g(x) into f(x) and solving for its output

First, we can plug the given x-value (4) into g(x):

`g(x) = 6x`

`g(4) = 6\cdot 4`

`g(4) = 24`

Next, we can plug the output from g(x) (24) into f(x):

`f(x) = 3√(x)`

`f(g(4)) = f(24) = 3√(24)`

`f(g(4)) = 3\cdot √(4)√(6)`

`f(g(4)) = 3\cdot 2\sqrt6`

`\boxed{f(g(4)) = 6\sqrt6}`

Note

`(f \circ g)(x)` is a shorthand notation for
`f(g(x))`.