Question

How do you find `f(g(4))` if `f(x)=2sqrt(x+3)` and `g(x)=-3x+1`?

Answer 1

`f(g(4))=4isqrt2`

Explanation:

First, find `g(4)`. Then, plug that value into `f(x)`.

Find `g(4)`:

`color(white)(xxxxxxx)g(4)=-3(4)+1`
`color(white)(xxxxxxx)g(4)=-11`

Find `f(g(4))`, which is equivalent to `f(-11)`:

`color(white)(xxxxxxx)f(-11)=2sqrt(-11+3)`
`color(white)(xxxxxxx)f(-11)=2sqrt(-8)`
`color(white)(xxxxxxx)f(-11)=2*2isqrt(2)`
`color(white)(xxxxxxx)f(-11)=4isqrt2`

Thus,

`color(white)(xxxxxxx)f(g(4))=4isqrt2`