Question

OLLEGE

>
For the given functions, find (fog)(x) and (gof)(x) and the domain of each.
f(x) = 4x + 1, g(x)=√x
(fog)(x) =
(gof)(x) =
The domain of fog is ☐.
(Type your answer in interval notation.)
The domain of g of is.
(Type your answer in interval notation. Use integers or fractions for any numbe

Answer 1

Part 1

`(f\circ g)(x)=f(√(x))=4√(x)+1`

We need to make sure the radical is defined, meaning the radicand has to be non-negative. Thus, the domain is
`\boxed{[0, \infty)}`

Part 2

`(g \circ f)(x)=g(4x+1)=√(4x+1)`

We need to make sure the radical is defined, meaning the radicand has to be non-negative. Thus,

`4x+1 \geq 0\\\\4x \geq -1\\\\x \geq -(1)/(4)`

Thus, the domain in interval notation is
`\boxed{\left[-(1)/(4), \infty)}`