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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 :

Medunno13

Part 1

[tex](f\circ g)(x)=f(\sqrt{x})=4\sqrt{x}+1[/tex]

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

Part 2

[tex](g \circ f)(x)=g(4x+1)=\sqrt{4x+1}[/tex]

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

[tex]4x+1 \geq 0\\\\4x \geq -1\\\\x \geq -\frac{1}{4}[/tex]

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

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